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Topic: Tsirelson space

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In the News (Sun 18 Aug 19)

 Most Recent Preprints   (Site not responding. Last check: 2007-10-12)
Stabilization of Tsirelson-type norms on $\ell_p$ spaces by Anna Maria Pelczar.
On Banach spaces whose duals are isomorphic to l_1 by Daniel M. Pellegrino.
Lipschitz spaces and $M$-ideals by Heiko Berninger and Dirk Werner.
www.math.okstate.edu /~alspach/banach/recent.html   (5508 words)

 Wikinfo | Lp space
spaces are spaces of p-power integrable functions, and corresponding sequence spaces.
Hilbert space, having major applications to Fourier series and quantum mechanics, as well as other fields.
The question of whether all Banach spaces have such an embedding was answered negatively by B. Tsirelson's construction of Tsirelson space in 1974.
www.wikinfo.org /wiki.php?title=Lp_space   (778 words)

 Lp space   (Site not responding. Last check: 2007-10-12)
Consider the set of all measurable functions from S to C (or R) whose absolute value to the p-th power has a finite Lebesgue integral.
spaces, in which the measure used in the integration in the definition is a counting measure and the measure space S is discrete.
spaces can be found embedded into many Banach spaces.
lp-space.iqnaut.net   (608 words)

 [No title]
Section~5 is devoted to the topological complexity of families of Banach spaces, in relation with universality problems and index theory.
The space $\nat^{\nat}$ consisting of all sequences of natural numbers, equipped with the product of the discrete topologies, is an important example of a Polish space, which is homeomorphic (through continued fractions) to the set $[0,1]\setminus\que$ equipped with the topology induced by the real line.
Weakly null sequences and asymptotic $\ell_p$ spaces} \end{center} \renewcommand{\thethm}{\thesection.\arabic{thm}} \renewcommand{\thesection}{3.\arabic{section}} \setcounter{equation}{0} \setcounter{thm}{0} \setcounter{section}{0} This section is devoted to the structure and the complexity, measured by ordinal scales, of weakly null sequences, as well as to the presentation of results related to the modern class of asymptotic $\ell_p$ spaces.
www.ma.utexas.edu /users/combs/Rosenthal/HB-format   (4704 words)

 My space : citing (geom)
1996 W.T. Gowers, "A new dichotomy for Banach spaces." Geom.
Schlumprecht, "Distortion and stabilized structure in Banach spaces; new geometric phenomena for Banach and Hilbert spaces." Proc.
Schlumprecht, "Distortion and asymptotic structure." In: Handbook of the geometry of Banach spaces (vol.
www.tau.ac.il /~tsirel/Research/myspace/cit_geom.html   (1113 words)

 Quantum mechanics - Wikipedia Mirror   (Site not responding. Last check: 2007-10-12)
However, if we restrict the particle to a region of space (the so-called "particle in a box" problem), the momentum observable will become discrete; it will only take on the values n \frac{h}{2 L}, where L is the length of the box, h is Planck's constant, and n is an arbitrary nonnegative integer number.
The exact nature of this Hilbert space is dependent on the system; for example, the state space for position and momentum states is the space of square-integrable functions, while the state space for the spin of a single proton is just the product of two complex planes.
Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate.
www.wiki-mirror.be /index.php/Quantum_mechanics   (5386 words)

 Tsirelson : "My space"
P.G. Casazza and T.J. Shura, "Tsirelson's space." Lecture Notes in Math., Vol.
Schlumprecht, "Distortion and stabilized structure in Banach spaces; new geometric phenomena for Banach and Hilbert spaces." Proceedings of the International Congress of Mathematicians, Zurich, Switzerland, 1994.
Tsirelson's space was the first truly nonclassical Banach space.
www.math.tau.ac.il /~tsirel/Research/myspace/main.html   (207 words)

 Basis Problem For Turbulent Actions - Farah (ResearchIndex)
If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
We use modified Tsirelson's spaces [3] to prove that there is no finite basis for turbulent Polish group actions.
5 On Tsirelson's space (context) - Casazza, Johnson et al.
citeseer.ist.psu.edu /farah98basis.html   (461 words)

 MSI Seminar List
The first example of a space showing that this hope was unfounded was provided by B. Tsirelson.
The ideas involved have since been used to construct an entire zoo of spaces exhibiting 'pathological' structure.
We discuss a class of models for the term structure of forward interest rates when the dynamics involve stochastic differential equations on a separable Hilbert space and the noise term is represented by a Hilbert space valued cylindrical Wiener process.
wwwmaths.anu.edu.au /calendar/03.05.17.cal.html   (329 words)

 Olga Vladimirskaya, PhDThesis, FU Berlin
Lyapunov´s which states that the range of every countably additive finite nonatomic vector measure valued in a finite dimensional space is a compact and convex set.
A Banach space is said to have the Lyapunov property if the closure of the range of every countably additive finite nonatomic vector measure valued in this space is a convex set.
It is proved that Banach spaces having this property have the Lyapunov property.
www.diss.fu-berlin.de /1999/42/indexe.html   (496 words)

 On Fréchet differentiability of Lipschitz maps between Banach spaces, Joram Lindenstrauss, David Preiss   (Site not responding. Last check: 2007-10-12)
Our aims are achieved by introducing a new class of null sets in Banach spaces (called $\Gamma$-null sets), whose definition involves both the notions of category and measure, and showing that the required differentiability holds almost everywhere with respect to it.
Our main result states that a Lipschitz map between separable Banach spaces is Fréchet differentiable $\Gamma$-almost everywhere provided that it is regularly Gâteaux differentiable $\Gamma$-almost everywhere and the Gâteaux derivatives stay within a norm separable space of operators.
The answer to the question is therefore positive in every space in which every $\sigma$-porous set is $\Gamma$-null.
projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.annm/1044909498   (275 words)

 Banach: Messages from 1994   (Site not responding. Last check: 2007-10-12)
It is shown that the Orlicz sequence space $h_M$ is isomorphic to a subspace of $C(\om^\om)$.
Up to a point, the theory of spaces which have this property is independent of the scalar field: the property is self-dual and any space with the property is a finite dimensional space of maximal distance to the Hilbert space of the same dimension.
Amongst them are constructions of a new prime Banach space, a space isomorphic to its subspaces of codimension two but not to its hyperplanes and a space isomorphic to its cube but not to its square.
www.math.okstate.edu /~alspach/banach/1994mes.html   (15931 words)

 Materials of spring schools
One chapter is devoted to the use of the Schauder basis in Banach spaces.
Nonseparable Banach spaces are studied in the chapter on weak compact generating, where basic results on projectional resolutions of identity, Markusevic bases and various types of compacta are discussed.
The notion of a locally convex space, metrizability, normability, finite dimensionality, separation, the bipolar theorem, the Mackey-Arens-Katetov theorem, the space of distributions, Choquet's representation theorem in metrizable case, the Banach-Dieudonne theorem, the Eberlein-Smulyan theorem, Kaplansky's theorem on countable tightness of the weak topology of a Banach space, the Banach-Stone theorem.
www.karlin.mff.cuni.cz /katedry/kma/ss/books/books.htm   (1219 words)

 Logic Colloquium Archive
We propose Chu spaces as a simple alternative to relational structures having the advantage that topology and duality are not only integral but fundamental to the approach.
We consider these ideals in the case when X is the Banach space not containing a copy of any of the classical spaces c_0 or ell_p (p in [1,infty)), constructed by B. Tsirelson.
The deeper understanding of this space achieved during the recent years has led to solutions of several long-standing open problems in Banach space theory.
www.math.ucla.edu /~hbe/logic-old.html   (10494 words)

 My space : citing (other)
1989 J.W. Baker, O.A. Slotterbeck, R. Aron, "An algorithm for computing the Tsirelson's space norm." Appendix to the book "Tsirelson's space" by P.G. Casazza and T.J. Shura, Lect.
1984 S.F. Bellenot, "The Banach space T and the fast growing hierarchy from logic." Israel J. Math.
1996 W.B. Johnson, J. Lindenstrauss, G. Schechtman, "Banach spaces determined by their uniform structures." Geom.
www.tau.ac.il /~tsirel/Research/myspace/cit_misc.html   (248 words)

 Figiel, Johnson: A uniformly convex Banach space which contains no $l_p$
Figiel, T. Johnson, W. A uniformly convex Banach space which contains no $l_p$.
: Banach spaces which can be given an equivalent uniformly convex norm.
: An example of an infinite dimensional Banach space non-isomorphic to its Cartesian square.
www.numdam.org /numdam-bin/item?id=CM_1974__29_2_179_0   (97 words)

 Klaus Floret Selected publications
Ultrastability of Ideals of Homogeneous Polynomials and Multilinear Mappings on Banach Spaces; to appear in: Proc.Amer.Math.Soc.
On Ideals of n-Homogeneous Polynomials on Banach Spaces, to appear in: Proc.
On Ideals of Polynomials and Multilinear Mappings between Banach Spaces; preprint Nov. 2000 (with D. García)
www.math.uni-oldenburg.de /personen/floret/publications.html   (215 words)

 News » Blog Archive » My Space NewWorkSpaces is a virtual space for   (Site not responding. Last check: 2007-10-12)
NewWorkSpaces is a virtual space for creating and sharing knowledge in community.
“My space” has appeared in my sole work on Banach spaces: B.S. When you decide to get a rental car for vacation or business, it would be great to think about some aspects while reserving to help make your trip more exciting.
Usually the prices are a primary consideration but there are some more important factors to think about.
www.getrentalcar.info /news/?p=19   (228 words)

 Definable Types Over Banach Spaces, José Iovino   (Site not responding. Last check: 2007-10-12)
We study connections between asymptotic structure in a Banach space and model theoretic properties of the space.
[12] Iovino, J., "Indiscernible sequences in Banach space geometry", preprint.
[15] Iovino, J., "Stable Banach spaces and Banach space structures.
projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.ndjfl/1107220672   (993 words)

 Document: VITA-2000
PUBLICATIONS: (With J. Baker and R. Aron) "Computing the Tsirelson Space Norm", Computer Aided Proofs in Analysis, edited by K. Meyer and D.
(With J. Baker and R. Aron)"An Algorithm for Computing the Tsirelson's Space Norm", published as Appendix B (44 pages) in Tsirelson's Space by P. Casazza and T. Shura, Lecture Notes in Mathematics, 1989.
1976 NSF Regional Conference on Banach Spaces, Kent State University 1975 Conference on Computers in Undergraduate Curricula, Texas Christian University, Texas.
cs.hiram.edu /~obie/vita.html   (2156 words)

 Amazon.com: "Texas Functional Analysis Seminar": Key Phrase page   (Site not responding. Last check: 2007-10-12)
[CO] P.G. Casazza and E. Odell, Tsirelson's space and minimal subspaces, Longhorn Notes: Texas Functional Analysis Seminar 1982-83, University of Texas, Austin, 61-72.
Isometries on Banach Spaces (Monographs & Surveys in Pure & Applied Math) by Richard J. Fleming, James E. Jamison
An Introduction to Metric Spaces and Fixed Point Theory by Mohamed A. Khamsi, William A. Kirk
www.amazon.com /phrase/Texas-Functional-Analysis-Seminar   (621 words)

 articles   (Site not responding. Last check: 2007-10-12)
3, 789--818., with Argyros, S. -- A note on certain equivalent norms on Tsirelson's space.
135 (2003), 29--81., with Argyros, S. and Petrakis, M. Distortion and spreading models in modified mixed Tsirelson spaces.
-- On the structure of a certain class of mixed Tsirelson spaces.
www.samos.aegean.gr /math/amanouss/articles/articles.html   (115 words)

 Amazon.com: "Longhorn Notes": Key Phrase page   (Site not responding. Last check: 2007-10-12)
Handbook of the Geometry of Banach Spaces : Volume 2 by Joram Lindenstrauss (Editor), W. Johnson (Editor)
Odell, Tsirelson space and minimal subspaces, Longhorn Notes University of Texas (1982-83),61-72.
Asymptotic Theory of Finite Dimensional Normed Spaces: Isoperimetric Inequalities in Riemannian Manifolds (Lecture Notes in Mathematics) by Vitali D. Milman, Gideon Schechtman
www.amazon.com /phrase/Longhorn-Notes   (534 words)

 Israel Journal of Mathematics, 2004(143 )
Type and infratype in symmetric sequence spaces / Talagrand, M
l1 -spreading models in mixed Tsirelson space / Leung, D H / Tang, W-K
On Banach spaces with unconditional bases / Lusky, W
www.ucm.es /BUCM/compludoc/W/10501/00212172_1.htm   (185 words)

 CJO - Abstract   (Site not responding. Last check: 2007-10-12)
We prove that the norm $\Vert\,{\cdot}\,\Vert_{n}$ of the space $T[\mathcal{S}_{n},\theta]$ and the norm $\Vert\,{\cdot}\,\Vert_{n}^{M}$ of its modified version $T_{M}[\mathcal{S}_{n},\theta]$ are 3-equivalent.
As a consequence, using the results of E. Odell and N. Tomczak-Jaegermann, we obtain that there exists a $K\,{<}\,\infty$ such that for all $n$, $\Vert\cdot\Vert_{n}^{M}$ does not $K-$ distort any subspace of Tsirelson's space $T$.
journals.cambridge.org /article_S0017089504001867   (86 words)

 Math arXiv: Search results   (Site not responding. Last check: 2007-10-12)
math.FA/0601542 More Mixed Tsirelson Spaces That Are Not Isomorphic To Their Modified Versions.
math.FA/0306133 \ell^1-spreading models in subspaces of mixed Tsirelson spaces.
math.FA/0110154 The Bourgain ell ^1-index of mixed Tsirelson space.
front.math.ucdavis.edu /author/Tang-W*   (207 words)

 Boris Tsirelson's home page
"My drift" (= Tsirelson's drift = Tsirelson's counterexample in the theory of stochastic differential equations)
"My space" (= Tsirelson's space = Tsirelson's counterexample in the theory of Banach spaces)
There is "Tsirelson street" in Tel Aviv; any comments?
www.math.tau.ac.il /~tsirel   (231 words)

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