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Topic: Selfadjoint operator

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	Operator algebra page of N. C. Phillips
		Operator algebras at the University of Southern Denmark (Odense).
		Operator Algebras Workgroup at the Institute of Mathematics at the Romanian Academy.
		Noncommutative geometry and operator algebras at Vanderbilt University.
	darkwing.uoregon.edu /~ncp/OpAlgResources/OpAlgPages/opalg.html (1256 words)

	Oxford University Press
		The new theory of operator spaces is presented early on and the text assembles the basic concepts, theory and methodologies needed to equip a beginning researcher in this area.
		In functional analysis, this has appeared notably under the name of `operator spaces', which is a variant of Banach spaces which is particularly appropriate for solving problems concerning spaces or algebras of operators on Hilbert space arising in 'noncommutative mathematics'.
		The rich interplay between spectral theory, operator theory, C*-algebra and von Neumann algebra techniques, and the influx of important ideas from related disciplines, such as pure algebra, Banach space theory, Banach algebras, and abstract function theory is highlighted.
	www.oup.com /ca/isbn/0-19-852659-8 (434 words)

	[No title]
		In the study of this problem an important part is played by the selfadjoint Friedrichs model operator $S_1:=t\cdot\,+ V$ acting in $L_2(\mathbb{R})$ (where $t\cdot$ stands for the operator of multiplication by the independent variable $t\in \mathbb{R}$, and $V$ is an integral operator with a continuous Hermitian kernel).
		Namely, it is of interest to investigate the singular spectrum of perturbations of the operators of multiplication by a function $f(t)$ of the independent variable (for example, $f(t)$ is equal to $\cos t$ or $t^2$).
		Below some conditions on the modulus of continuity $\omega(t)$ of the perturbation operator $V$ are given guaranteeing the absolute continuity of the spectrum of the operator $A_m$ on the interval $[0,+\infty)$ near zero.
	www.univie.ac.at /EMIS/journals/EJDE/conf-proc/13/i1/iakovlev-tex (2828 words)

	RVRomanov (Site not responding. Last check: 2007-10-06)
		It is shown that the essential spectrum of the operator is absolutely continuous with one possible spectral singularity at the point 0.
		The absolutely continuous component of the operator is shown to be similar to a direct sum of a selfadjoint operator and an operator with spectrum of finite multiplicity.
		We also study the geometry of invariant subspaces of the operator in the presence of the spectral singularity.
	www.cs.cf.ac.uk /Gregynog02/RVRomanov (129 words)

	Allan Donsig's research page
		The commutative self-adjoint operator algebras are the natural function algebras on a topological space or a measure space.
		Motivated partly by this and partly by other topics, the study of non-commutative (selfadjoint) operator algebras can be viewed as `non-commutative topology' and `non-commutative measure theory'.
		If the algebra is also a CSL algebra, we scharacterize when the first homology group of the algebra is contained in the first homology group of the (4,4) entry; in these cases, the only obstruction to a derivation being inner arises from the (4,4) entry.
	www.math.unl.edu /~adonsig1/research.html (2559 words)

	AMCA: J-selfadjoint ordinary differential operators similar to selfadjoint operators by Ilia Karabash (Site not responding. Last check: 2007-10-06)
		is similar to a selfadjoint operator if p(t) is a nonnegative polynomial with at most one real root.
		Malamud M. A criterion of the similarity of a closed operator to a selfadjoint operator // Ukrainian Math.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/d/o/88.htm (244 words)

	[No title] (Site not responding. Last check: 2007-10-06)
		Together with the latter theorem, the result of the present paper suggests that the existence of an absolutely continuous spectrum for dissipative ordinary differential operators is equivalent to having a scattering theory.
		The spectral averaging method, as developed by Last-Simon, seems to be only applicable to operators semi-bounded below, while a selfadjoint operator corresponding to a differential expression of the form (\ref{eq:1.1}) is never semi-bounded.
		Preliminaries: Absolutely Continuous Subspace} Let $ H $ be a Hilbert space and $ L $ be a maximal dissipative operator in $ H $ of the form $ L = A + i V $, $ A = A^* $, $ V \ge 0 $ is bounded.
	www.ma.utexas.edu /mp_arc/html/papers/04-230 (1820 words)

	Leiba Rodman: List of Publications Arranged by Topics
		On analytic equivalence of operator polynomials, Integral Equations and Operator Theory, 2 (1979), 48-61.
		On factorization of operator polynomials and analytic operator functions, Rocky Mountain Journal of Mathematics, 16 (1986), 153-162.
		On factorization of selfadjoint operator polynomials, Proceedings of Symposia in Pure Mathematics, 51 (1990), 295-306.
	www.math.wm.edu /~lxrodm/topics.html (12604 words)

	[No title]
		In the complex case, selfadjoint matrices are often called {\em Hermitean matrices}.\\ \noindent{\em Note}: By 11.6, an operator $T$ is selfadjoint whenever the matrix $[T]_B$ is selfadjoint for any (and then every) ONB $B$.
		A selfadjoint operator $T:V\to V$ is said to be {\em positive definite} if $\langle Tu,u\rangle >0$ for all $u\neq 0$.
		The linear operator $P$ on $V$ defined by $Pv=w-w'$ is called a {\em reflection} (or {\em reflector}) across the hyperplane $W$.
	www.math.uab.edu /chernov/teaching/632notes (10997 words)

	Abstract - Change of Jordan structure (Site not responding. Last check: 2007-10-06)
		In 1980 Markus and Parilis, and den Boer and Thijsse, confirming an earlier conjecture of Gohberg and Kaashoek, obtained a description of the possible domain of variation of the lengths of Jordan chains (partial multiplicities) of linear operators and analytic operator functions, and of Gohberg-Kaashoek numbers, under small perturbations.
		In this paper similar problems are extended to the classes of G-selfadjoint operators, and selfadjoint operator functions.
		The role played by the Gohberg-Kaashoek numbers in the description of the behavior of the lattice of all invariant subspaces, under a small perturbation of a matrix, is revealed in [O89a].
	www.math.uconn.edu /~olshevsk/abstracts/cjs.html (158 words)

	[No title]
		adjoint +------------------------------------------------------------ The adjoint of a bounded linear operator A on a Hilbert space is the unique operator B which satisfies (Ax,y)=(x,By) for all x,y in H. One calls the adjoint A^*.
		Important examples are bounded linear operators, linear operators which also continuous maps.
		norm +------------------------------------------------------------ The norm of a bounded linear operator A on a Hilbert space H is defined as A
	www.math.harvard.edu /~knill/sofia/data/functionalanalysis.txt (355 words)

	Directory of operator algebraist home pages
		Operator algebraists directory at the Institute of Mathematics of the Romanian Academy, maintained by Birant Ramazan.
		Operator theory on Krein spaces, model theory for families of operators.
		Operator algebra ideas applied to the study of wavelets, statistical mechanics, representation theory, and quantum physics.
	darkwing.uoregon.edu /~ncp/OpAlgResources/HomePageDir/homepagedir.html (1056 words)

	The Univ. of Iowa, Functional Analysis and Operator Theory Group (Site not responding. Last check: 2007-10-06)
		His interests are in operator algebras, specializing in non-selfadjoint operator algebras.
		He is interested in all aspects of operator theory and operator algebra.
		A large portion of his research is devoted to coordinate representation of operator algebras using groupoids and related technology.
	www.math.uiowa.edu /faculty/researchGroups/fcnlanal.htm (168 words)

	Citebase - Non-selfadjoint Operator Algebras generated by Weighted Shifts on Fock Space
		We investigate the unital weak operator topology closed algebras they generate.
		The commutant can be described in terms of weighted right creation operators when the weights satisfy a condition specific to the noncommutative setting.
		We prove these algebras are reflexive when the eigenvalues for the adjoint algebra include an open set in complex n-space, and provide a new elementary proof of reflexivity for the unweighted case.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0309371 (606 words)

	belyi (Site not responding. Last check: 2007-10-06)
		Realization theory of different classes of operator-valued (matrix) functions as transfer operator-valued functions of linear systems plays an important role in modern operator, system, control, and scattering theories.
		Almost all realizations in the modern theory of non-selfadjoint operators and its applications deal with systems (operator colligations) the main operator of which is a bounded linear operator.
		The case with an unbounded non-selfadjoint operator as a main operator in a corresponding system has not been investigated thoroughly because of a number of essential difficulties usually connected with unbounded.
	math.la.asu.edu /~sf2000/belyi.html (147 words)

	Citebase - Diagonalizing operators with reflection symmetry (Site not responding. Last check: 2007-10-06)
		We show that there is then a Hilbert space \mathcalH(\mathcalK), a contractive operator W:\mathcalK→\mathcalH(\mathcalK), and a selfadjoint operator S=S(U) in \mathcalH(\mathcalK) such that W
		For that case, we describe the spectrum of the selfadjoint operator S(U) in terms of structural properties of U. In the model, U will be realized as a unitary scaling operator of the form f(x)\mapsto f(cx), c>1, and the spectrum of S(U
		Citation coverage and analysis is incomplete and hit coverage and analysis is both incomplete and noisy.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/9908021 (560 words)

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