Conditions under which a Cylindrical Measure on a Dual Banach Space May Be Extended to a Radon Measure

1980 ◽  
Vol 24 (3) ◽  
pp. 582-587 ◽  
Author(s):  
Yu. N. Vladimirskii
Keyword(s):  
Banach Space ◽  
Radon Measure ◽  
Cylindrical Measure ◽  
Dual Banach Space

Completions of Boolean algebras of projections and weak-star closures of C*-algebras on dual Banach spaces

2011 ◽  
Vol 54 (2) ◽  
pp. 515-529
Author(s):  
Philip G. Spain
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Boolean Algebras ◽  
C Algebra ◽  
C Algebras ◽  
Weak Star ◽  
Weakly Closed ◽  
Operator Closure ◽  
Dual Banach Space ◽  
Completion Theorem

AbstractPalmer has shown that those hermitians in the weak-star operator closure of a commutative C*-algebra represented on a dual Banach space X that are known to commute with the initial C*-algebra form the real part of a weakly closed C*-algebra on X. Relying on a result of Murphy, it is shown in this paper that this last proviso may be dropped, and that the weak-star closure is even a W*-algebra.When the dual Banach space X is separable, one can prove a similar result for C*-equivalent algebras, via a ‘separable patch’ completion theorem for Boolean algebras of projections on such spaces.

Biholomorphic Mappings on Banach Spaces

2019 ◽  
Vol 62 (4) ◽  
pp. 913-924
Author(s):  
H. Carrión ◽  
P. Galindo ◽  
M. L. Lourenço
Keyword(s):  
Banach Space ◽  
Hilbert Space ◽  
Open Subset ◽  
Separable Hilbert Space ◽  
Derivative Operator ◽  
Infinite Dimensional ◽  
Dimensional Version ◽  
Dual Banach Space ◽  
Bounded Convex ◽  
Power Bounded

AbstractWe present an infinite-dimensional version of Cartan's theorem concerning the existence of a holomorphic inverse of a given holomorphic self-map of a bounded convex open subset of a dual Banach space. No separability is assumed, contrary to previous analogous results. The main assumption is that the derivative operator is power bounded, and which we, in turn, show to be diagonalizable in some cases, like the separable Hilbert space.

scholarly journals To what extent does the dual Banach space E′ determine the polynomials over E?

2000 ◽  
Vol 38 (2) ◽  
pp. 343-354 ◽  
Author(s):  
Silvia Lassalle ◽  
Ignacio Zalduendo
Keyword(s):  
Banach Space ◽  
Dual Banach Space

scholarly journals The states of a Banach algebra generate the dual

1971 ◽  
Vol 17 (4) ◽  
pp. 341-344 ◽  
Author(s):  
Allan M. Sinclair
Keyword(s):  
Banach Space ◽  
Banach Algebra ◽  
Linear Combination ◽  
Linear Functional ◽  
Measure Theory ◽  
Complex Field ◽  
Continuous Linear ◽  
Continuous Linear Functional ◽  
Unital Banach Algebra ◽  
Dual Banach Space

In this paper we prove that the states of a unital Banach algebra generate the dual Banach space as a linear space (Theorem 2). This is a result of R. T. Moore (4, Theorem 1(a)) who uses a decomposition of measures in his proof. In the proof given here the measure theory is replaced by a Hahn-Banach separation argument. We shall let A denote a unital Banach algebra over the complex field, and D(1) denote {f ∈ A′: ‖f‖ = f(1) = 1} where A′ is the dual of A. The motivation of Moore's results is the theorem that in a C*-algebra every continuous linear functional is a linear combination of four states (the states are the elements of D(1)) (see (2, 2.6.4, 2.1.9, 1.1.10)).

On the Duality of Operator Spaces

1995 ◽  
Vol 38 (3) ◽  
pp. 334-346 ◽  
Author(s):  
Christian Le Merdy
Keyword(s):  
Banach Space ◽  
Von Neumann Algebras ◽  
Related Result ◽  
Space Structure ◽  
Operator Space ◽  
Operator Spaces ◽  
Bounded Operators ◽  
Von Neumann ◽  
Operator Space Structure ◽  
Dual Banach Space

AbstractWe prove that given an operator space structure on a dual Banach space Y*, it is not necessarily the dual one of some operator space structure on Y. This allows us to show that Sakai's theorem providing the identification between C*-algebras having a predual and von Neumann algebras does not extend to the category of operator spaces. We also include a related result about completely bounded operators from B(ℓ2)* into the operator Hilbert space OH.

A Banach–Stone theorem for spaces of weak* continuous functions

1985 ◽  
Vol 101 (3-4) ◽  
pp. 203-206 ◽  
Author(s):  
Michael Cambern
Keyword(s):  
Banach Space ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Continuous Functions ◽  
Convex Banach Space ◽  
Uniformly Convex ◽  
Hausdorff Spaces ◽  
Space Of Continuous Functions ◽  
Dual Banach Space ◽  
Stone Theorem

SynopsisIf X is a compact Hausdorff space and E a dual Banach space, let C(X, Eσ*) denote the Banach space of continuous functions F from X to E when the latter space is provided with its weak * topology, normed by . It is shown that if X and Y are extremally disconnected compact Hausdorff spaces and E is a uniformly convex Banach space, then the existence of an isometry between C(X, Eσ*) and C(Y, Eσ*) implies that X and Y are homeomorphic.

scholarly journals Fixed point properties for semigroups of nonexpansive mappings on convex sets in dual Banach spaces

2018 ◽  
Vol 17 (1) ◽  
pp. 67-87
Author(s):  
Anthony To-Ming Lau ◽  
Yong Zhang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Convex Subset ◽  
Convex Sets ◽  
Compact Convex ◽  
Nonexpansive Mappings ◽  
Point Property ◽  
Fixed Point Properties ◽  
Dual Banach Space ◽  
Standing Problem

Abstract It has been a long-standing problem posed by the first author in a conference in Marseille in 1990 to characterize semitopological semigroups which have common fixed point property when acting on a nonempty weak* compact convex subset of a dual Banach space as weak* continuous and norm nonexpansive mappings. Our investigation in the paper centers around this problem. Our main results rely on the well-known Ky Fan’s inequality for convex functions.

Predual of the Multiplier Algebra of Ap(G) and Amenability

2004 ◽  
Vol 56 (2) ◽  
pp. 344-355 ◽  
Author(s):  
Tianxuan Miao
Keyword(s):  
Banach Space ◽  
Compact Group ◽  
Linear Span ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Multiplier Algebra ◽  
Norm Closure ◽  
Multiplier Space ◽  
Dual Banach Space

AbstractFor a locally compact group G and 1 < p < ∞, let Ap(G) be the Herz-Figà-Talamanca algebra and let PMp(G) be its dual Banach space. For a Banach Ap(G)-module X of PMp(G), we prove that the multiplier space ℳ(Ap(G); X*) is the dual Banach space of QX, where QX is the norm closure of the linear span Ap(G)X of u f for u 2 Ap(G) and f ∈ X in the dual of ℳ(Ap(G); X*). If p = 2 and PFp(G) ⊆ X, then Ap(G)X is closed in X if and only if G is amenable. In particular, we prove that the multiplier algebra MAp(G) of Ap(G) is the dual of Q, where Q is the completion of L1(G) in the ‖ · ‖M-norm. Q is characterized by the following: f ∈ Q if an only if there are ui ∈ Ap(G) and fi ∈ PFp(G) (i = 1; 2, … ) with such that on MAp(G). It is also proved that if Ap(G) is dense in MAp(G) in the associated w*-topology, then the multiplier norm and ‖ · ‖Ap(G)-norm are equivalent on Ap(G) if and only if G is amenable.

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