Weak sequential completeness in Banach $$C(K)$$ C ( K ) -modules of finite multiplicity

Positivity ◽  
2015 ◽  
Vol 21 (2) ◽  
pp. 739-753 ◽  
Author(s):  
Arkady Kitover ◽  
Mehmet Orhon
Keyword(s):  
Finite Multiplicity ◽  
Sequential Completeness

scholarly journals In what spaces is every closed normal cone regular?

1970 ◽  
Vol 17 (2) ◽  
pp. 121-125 ◽  
Author(s):  
C. W. McArthur
Keyword(s):  
Banach Space ◽  
Convex Space ◽  
Unconditional Basis ◽  
Normal Cone ◽  
Closed Subspace ◽  
Locally Convex Space ◽  
Regular Part ◽  
Fréchet Space ◽  
Sequential Completeness ◽  
Locally Convex

It is known (13, p. 92) that each closed normal cone in a weakly sequentially complete locally convex space is regular and fully regular. Part of the main theorem of this paper shows that a certain amount of weak sequential completeness is necessary in order that each closed normal cone be regular. Specifically, it is shown that each closed normal cone in a Fréchet space is regular if and only if each closed subspace with an unconditional basis is weakly sequentially complete. If E is a strongly separable conjugate of a Banach space it is shown that each closed normal cone in E is fully regular. If E is a Banach space with an unconditional basis it is shown that each closed normal cone in E is fully regular if and only if E is the conjugate of a Banach space.

scholarly journals Finite multiplicity theorems for induction and restriction

2013 ◽  
Vol 248 ◽  
pp. 921-944 ◽  
Author(s):  
Toshiyuki Kobayashi ◽  
Toshio Oshima
Keyword(s):  
Finite Multiplicity

scholarly journals Unitary Equivalence and Similarity to Jordan Models for Weak Contractions of Class C0

2015 ◽  
Vol 67 (1) ◽  
pp. 132-151
Author(s):  
Raphaël Clouâtre
Keyword(s):  
Blaschke Product ◽  
Main Tool ◽  
Unitary Equivalence ◽  
Finite Multiplicity ◽  
Minimal Function ◽  
Boundary Representations ◽  
Class C

AbstractWe obtain results on the unitary equivalence of weak contractions of class C0 to their Jordan models under an assumption on their commutants. In particular, our work addresses the case of arbitrary finite multiplicity. The main tool in this paper is the theory of boundary representations due to Arveson. We also generalize and improve previously known results concerning unitary equivalence and similarity to Jordan models when the minimal function is a Blaschke product.

scholarly journals Sequential completeness of quotient groups

2000 ◽  
Vol 61 (1) ◽  
pp. 129-150 ◽  
Author(s):  
Dikran Dikranjan ◽  
Michael Tkačenko
Keyword(s):  
Abelian Group ◽  
Direct Products ◽  
Topological Groups ◽  
Complete Group ◽  
Sequential Completeness ◽  
Algebraic Properties ◽  
Countable Compactness ◽  
Quotient Groups

We discuss various generalisations of countable compactness for topological groups that are related to completeness. The sequentially complete groups form a class closed with respect to taking direct products and closed subgroups. Surprisingly, the stronger version of sequential completeness called sequential h-completeness (all continuous homomorphic images are sequentially complete) implies pseudocompactness in the presence of good algebraic properties such as nilpotency. We also study quotients of sequentially complete groups and find several classes of sequentially q-complete groups (all quotients are sequentially complete). Finally, we show that the pseudocompact sequentially complete groups are far from being sequentially q-complete in the following sense: every pseudocompact Abelian group is a quotient of a pseudocompact Abelian sequentially complete group.

Symbols in Berezin quantization for representation operators

2021 ◽  
pp. 296-304
Author(s):  
Vladimir F. Molchanov ◽  
Svetlana V. Tsykina
Keyword(s):  
Homogeneous Space ◽  
Lie Algebra ◽  
Grassmann Manifold ◽  
Homogeneous Spaces ◽  
Finite Multiplicity ◽  
Basic Notion ◽  
Berezin Quantization ◽  
Algebraic Version ◽  
Enveloping Algebra ◽  
Algebra Of Operators

The basic notion of the Berezin quantization on a manifold M is a correspondence which to an operator A from a class assigns the pair of functions F and F^♮ defined on M. These functions are called covariant and contravariant symbols of A. We are interested in homogeneous space M=G/H and classes of operators related to the representation theory. The most algebraic version of quantization — we call it the polynomial quantization — is obtained when operators belong to the algebra of operators corresponding in a representation T of G to elements X of the universal enveloping algebra Env g of the Lie algebra g of G. In this case symbols turn out to be polynomials on the Lie algebra g. In this paper we offer a new theme in the Berezin quantization on G/H: as an initial class of operators we take operators corresponding to elements of the group G itself in a representation T of this group. In the paper we consider two examples, here homogeneous spaces are para-Hermitian spaces of rank 1 and 2: a) G=SL(2;R), H — the subgroup of diagonal matrices, G/H — a hyperboloid of one sheet in R^3; b) G — the pseudoorthogonal group SO_0 (p; q), the subgroup H covers with finite multiplicity the group SO_0 (p-1,q -1)×SO_0 (1;1); the space G/H (a pseudo-Grassmann manifold) is an orbit in the Lie algebra g of the group G.

On the Weak Sequential Completeness of the Spaces of Radon Measures

1985 ◽  
Vol 29 (1) ◽  
pp. 142-147 ◽  
Author(s):  
Yu. L. Daletskii ◽  
O. G. Smolyanov
Keyword(s):  
Radon Measures ◽  
Sequential Completeness

scholarly journals Existence results for fractional p-Laplacian problems via Morse theory

2016 ◽  
Vol 9 (2) ◽  
Author(s):  
Antonio Iannizzotto ◽  
Shibo Liu ◽  
Kanishka Perera ◽  
Marco Squassina
Keyword(s):  
Phase Transition ◽  
Game Theory ◽  
Morse Theory ◽  
Fractional Laplacian ◽  
Existence Results ◽  
Nonlocal Problems ◽  
Finite Multiplicity ◽  
Topological Methods ◽  
Multiplicity Results ◽  
Linear Problems

AbstractWe investigate a class of quasi-linear nonlocal problems, including as a particular case semi-linear problems involving the fractional Laplacian and arising in the framework of continuum mechanics, phase transition phenomena, population dynamics and game theory. Under different growth assumptions on the reaction term, we obtain various existence as well as finite multiplicity results by means of variational and topological methods and, in particular, arguments from Morse theory.

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