On Banach modules I

Kaijser, Sten

doi:10.1017/s0305004100058904

Cited by 17 publications

(14 citation statements)

References 24 publications

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“…As we mentioned in the introduction, such representations are always subordinate to W AP (A). Our result strengthens Kaijser's result [26,Lemma 4.12] by replacing the identity of A with a bounded approximate identity.…”

Section: Weakly Almost Periodic Functionalssupporting

confidence: 87%

“…For a (not necessarily involutive) Banach algebra A, the close connections between representations of A on the one hand, and elements of the dual space A * on the other hand, have been studied in several papers including Fell [17], Bonsall and Duncan [4,5], Young [38], Lau [28], Kaijser [26], Duncan andÜlger [15], and more recently, Runde [32] and Daws [12].…”

Section: Introductionmentioning

confidence: 99%

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Representations of Banach algebras subordinate to topologically introverted spaces

Filali

Neufang

Monfared

2015

Trans. Amer. Math. Soc.

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Let A be a Banach algebra, X a closed subspace of A * , Y a dual Banach space with predual Y * , and π a continuous representation of A on Y . We call π subordinate to X if each coordinate function π y,λ ∈ X, for all y ∈ Y, λ ∈ Y * . If X is topologically left (right) introverted and Y is reflexive, we show the existence of a natural bijection between continuous representations of A on Y subordinate to X, and normal representations of X * on Y . We show that if A has a bounded approximate identity, then every weakly almost periodic functional on A is a coordinate function of a continuous representation of A subordinate to W AP (A). We show that a function f on a locally compact group G is left uniformly continuous if and only if it is the coordinate function of the conjugate representation of L 1 (G), associated to some unitary representation of G. We generalize the latter result to an arbitrary Banach algebra with bounded right approximate identity. We prove the functionals in LU C(A) are all coordinate functions of some norm continuous representation of A on a dual Banach space.

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Section: Weakly Almost Periodic Functionalssupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Representations of Banach algebras subordinate to topologically introverted spaces

Filali

Neufang

Monfared

2015

Trans. Amer. Math. Soc.

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“…We note that in [20,Proposition 4.9], Kaijser explores similar ideas to the above proposition. Furthermore, the equivalence of (1) and (2) is established in [22,Lemma 1.4] in the case of commutative Banach algebras.…”

Section: Basic Properties Of Wap and Dual Banach Algebrasmentioning

confidence: 72%

Dual Banach algebras: representations and injectivity

Daws¹

2007

Studia Math.

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We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C *and W * -algebras; we show that interpolation space techniques can be used in the place of GNS type arguments. We define a notion of injectivity for dual Banach algebras, and show that this is equivalent to Connes-amenability. We conclude by looking at the problem of defining a well-behaved tensor product for dual Banach algebras.

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“…The following result was first shown by Young in [21], building upon [5], and was recast in terms of the real interpolation method by Kaiser in [12] (see also the similar arguments in [6]). …”

Section: Application To Weakly Almost Periodic Elementsmentioning

confidence: 78%

Weakly almost periodic functionals on the measure algebra

Daws

2009

Math. Z.

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It is shown that the collection of weakly almost periodic functionals on the convolution algebra of a commutative Hopf von Neumann algebra is a C$^*$-algebra. This implies that the weakly almost periodic functionals on $M(G)$, the measure algebra of a locally compact group $G$, is a C$^*$-subalgebra of $M(G)^* = C_0(G)^{**}$. The proof builds upon a factorisation result, due to Young and Kaiser, for weakly compact module maps. The main technique is to adapt some of the theory of corepresentations to the setting of general reflexive Banach spaces.Comment: 13 pages; added references and fixed typo

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On Banach modules I

Cited by 17 publications

References 24 publications

Representations of Banach algebras subordinate to topologically introverted spaces

Representations of Banach algebras subordinate to topologically introverted spaces

Dual Banach algebras: representations and injectivity

Weakly almost periodic functionals on the measure algebra

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