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Topic: Seminorm


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  PlanetMath: seminorm
A seminorm differs from a norm in that it is permitted that
Conversely, suppose that the seminorm function is homogeneous, and that the unit ball is convex.
This is version 16 of seminorm, born on 2002-02-20, modified 2006-09-07.
planetmath.org /encyclopedia/SemiNorm2.html   (249 words)

  
 Kolmogorov space
The problem is that this is not really a norm, only a seminorm[?], because there are functions other than the zero function[?] whose (semi)norms are zero.
This constructs a quotient space of the original seminormed vector space, and this quotient is a normed vector space.
From the point of view of topology, the seminormed vector space that we started with has a lot of extra structure; for example, it's a vector space, and it has a seminorm, and these define a pseudometric and a uniform structure that are compatible with the topology.
ebroadcast.com.au /lookup/encyclopedia/ko/Kolmogorov_equivalence.html   (851 words)

  
 PlanetMath: example of pseudometric space
See Also: seminorm, vector space, metric space, metric
Cross-references: seminorm, vector space, pseudometric, distance, points, metric space, pseudometric space, satisfies, triangle inequality, real numbers, function
This is version 2 of example of pseudometric space, born on 2004-10-02, modified 2004-10-03.
planetmath.org /encyclopedia/TrivialPseudometric.html   (111 words)

  
 [No title]
This norm induces a seminorm on singular homology.
By Lemma (1.13) the seminorm k k1on homology with real coefficients in- duced by the `1-norm on the singular chain complex is functorial.
Gro- mov conjectured that this phenomenon occurs for all functorial seminorms [Gromov4, Remark in 5.35]: Conjecture.
www.math.purdue.edu /research/atopology/Strohm/diploma_main.txt   (17691 words)

  
 Theory NormedSpace (Isabelle2005: October 2005)
qed subsection {* Norms *} text {* A \emph{norm} @{text "\·\"} is a seminorm that maps only the @{text 0} vector to @{text 0}.
*} locale norm = seminorm + assumes zero_iff [iff]: "x ∈ V ==> (\x\ = 0) = (x = 0)" subsection {* Normed vector spaces *} text {* A vector space together with a norm is called a \emph{normed space}.
with subset show "seminorm F norm" by (simp add: seminorm_def) have "norm_axioms E norm".
www.cl.cam.ac.uk /Research/HVG/Isabelle/dist/library/HOL/HOL-Complex/HahnBanach/NormedSpace.html   (269 words)

  
 Nuclear space - Wikipedia, the free encyclopedia
The topology on them can be defined by a family of seminorms whose unit balls decrease rapidly in size.
For any seminorm, the unit ball is a closed convex symmetric neighborhood of 0, and conversely any closed convex symmetric neighborhood of 0 is the unit ball of some seminorm.
It is not necessary to check this condition for all seminorms p; it is sufficient to check it for a set of seminorms that generate the topology.
en.wikipedia.org /wiki/Nuclear_space   (1182 words)

  
 Proceedings of the American Mathematical Society
A seminorm with square property on a complex associative algebra is submultiplicative
Abstract: The result stated in the title is proved as a consequence of an appropriate generalization replacing the square property of a seminorm with a similar weaker property which implies an equivalence to the supnorm of all continuous functions on a compact Hausdorff space also.
S.J.Bhatt, A seminorm with square property on a Banach algebra is submultiplicative, Proc.Amer.Math.Soc.
www.mathaware.org /proc/2002-130-07/S0002-9939-01-06278-5/home.html   (208 words)

  
 U.Krallert; G.Wanka : Efficiency in seminorm location problems
In this work connections between efficiency sets of multiobjective location optimization problems and solutions of single objective location optimization problems in Hausdorff locally convex topological vector spaces with seminorms as distance functions are given.
because several seminorms or even families of seminorms are used simultaneously instead of only one seminorm for the single objective location optimization problem, then the ideal solution of this multiobjective location optimization problems should be considered.
For only one seminorm the well-known multiobjective location optimization problem arises as a collection of single criteria.
www.mathematik.tu-chemnitz.de /preprint/1997/PREPRINT_27.html   (217 words)

  
 [No title]
If in addition our collection of seminorms is countable we call our locally convex topological vector space a "Frechet space".
Here there is one seminorm ._v on V* for each element v of V; the seminorm ._v is defined by f_v = f(v).
By this means the space of distributions and the space of hyperfunctions on the circle become locally convex topological vector spaces.
www.math.niu.edu /~rusin/known-math/98/TVS   (906 words)

  
 v4n1
Bounds are obtained for the Chebychev functional using what is termed as the Ostrowski seminorm which is related to an inequality developed by Ostrowski.
The Ostrowski seminorm is also compared to the
In this paper, we study the influence of the perturbing term in equation
rgmia.vu.edu.au /v4n1.html   (791 words)

  
 The Trade-Off Between Regularity And Stabilization In Tikhonov Regularization - Nair, Hegland, Anderssen (ResearchIndex)   (Site not responding. Last check: 2007-11-03)
If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
Abstract: When deriving rates of convergence for the approximations generated by the application of Tikhonov regularization to ill--posed operator equations, assumptions must be made about the nature of the stabilization (i.e., the choice of the seminorm in the Tikhonov regularization) and the regularity of the least squares solutions which one looks for.
In fact, it is clear from works of Hegland, Engl and Neubauer and Natterer that, in terms of the rate of convergence, there is a trade--off between...
citeseer.ist.psu.edu /nair94tradeoff.html   (644 words)

  
 Amazon.com: "seminorm topology": Key Phrase page   (Site not responding. Last check: 2007-11-03)
See all pages with references to seminorm topology.
space X, the map defined by p, (x) = I f(x)l (x E X) is a seminorm on X. The seminorm topology determined by the p, as f runs through the linear space X* of all linear forms on X is a...
Key Phrases in this book: bornivorous disk, ultrabornological spaces, barreled spaces, maximal filterbase, disked hull, absorbent disk, nonarchimedean seminorm, weak representation theorem, closed linear map, extendible space, bornivorous string, neighborhood subbase (See more)
www.amazon.com /phrase/seminorm-topology   (392 words)

  
 Math Forum Discussions
>>Does there exist a "non-trivial" seminorm in R(n,n), such that for every A, B
Or doesn't a seminorm have to satisfy the
The Math Forum is a research and educational enterprise of the Drexel School of Education.
mathforum.org /kb/thread.jspa?messageID=3915173&tstart=0   (89 words)

  
 Hahn-Banach Theorem
In fact, we'll be able to do this quite generally, i.e., for any seminorm.
Every seminorm is sublinear functional but not conversely.
Thus, we will have a suitable extension as long as
www.math.unl.edu /~s-bbockel1/928/node23.html   (137 words)

  
 A Circulant Seminorm Representation on the Unit Cube   (Site not responding. Last check: 2007-11-03)
A Circulant Seminorm Representation on the Unit Cube
can be reduced to a sum of 'partial' seminorms as follows:
can be substituted by the following sum of the one-dimensional circulant seminorms:
hej.sze.hu /ANM/ANM-980205-A/anm980205a/node4.html   (143 words)

  
 CiteULike: On One Extremal Problem for a Seminorm on the Space l1 with Weight   (Site not responding. Last check: 2007-11-03)
CiteULike: On One Extremal Problem for a Seminorm on the Space l1 with Weight
On One Extremal Problem for a Seminorm on the Space l1 with Weight
Note: You or your institution must have access rights to this article.
www.citeulike.org /article/446107   (62 words)

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