Displaying similar documents to “A direct decomposition of the measure algebra of a locally compact abelian group”

Spaces of type H ∞ + C

Walter Rudin (1975)

Annales de l'institut Fourier

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A simple theorem is proved which states a sufficient condition for the sum ot two closed subspaces of a Banach space to be closed. This leads to several analogues of Sarason’s theorem which states that H ∞ + C is a closed subalgebra of L ∞ . In these analogues, the unit circle is replaces by other groups, and the unit disc is replaced by polydiscs or by balls in spaces of several complex variables. Sums of closed ideals in Banach algebras are also studied.

A characterization of the minimal strongly character invariant Segal algebra

Viktor Losert (1980)

Annales de l'institut Fourier

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For a locally compact, abelian group G , we study the space S 0 ( G ) of functions on G belonging locally to the Fourier algebra and with l 1 -behavior at infinity. We give an abstract characterization of the family of spaces { S 0 ( G ) : G abelian } by its hereditary properties.

Spectrum of commutative Banach algebras and isomorphism of C*-algebras related to locally compact groups

Zhiguo Hu (1998)

Studia Mathematica

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Let A be a semisimple commutative regular tauberian Banach algebra with spectrum Σ A . In this paper, we study the norm spectra of elements of s p a n ¯ Σ A and present some applications. In particular, we characterize the discreteness of Σ A in terms of norm spectra. The algebra A is said to have property (S) if, for all φ ∈ ¯ Σ A 0 , φ has a nonempty norm spectrum. For a locally compact group G, let ℳ 2 d ( Ĝ ) denote the C*-algebra generated by left translation operators on L 2 ( G ) and G d denote the discrete group G. We prove...

On decompositions of Banach spaces into a sum of operator ranges

V. Fonf, V. Shevchik (1999)

Studia Mathematica

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It is proved that a separable Banach space X admits a representation X = X 1 + X 2 as a sum (not necessarily direct) of two infinite-codimensional closed subspaces X 1 and X 2 if and only if it admits a representation X = A 1 ( Y 1 ) + A 2 ( Y 2 ) as a sum (not necessarily direct) of two infinite-codimensional operator ranges. Suppose that a separable Banach space X admits a representation as above. Then it admits a representation X = T 1 ( Z 1 ) + T 2 ( Z 2 ) such that neither of the operator ranges T 1 ( Z 1 ) , T 2 ( Z 2 ) contains an infinite-dimensional closed subspace...

The order structure of the space of measures with continuous translation

Gérard L. G. Sleijpen (1982)

Annales de l'institut Fourier

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Let G be a locally compact group, and let ∥ ∥ ∞ B be a function norm on L 1 ( G ) loc such that the space L ∞ ( G , B ) of all locally integrable functions with finite ∥ ∥ ∞ B -norm is an invariant solid Banach function space. Consider the space L RUC ( G , B ) of all functions in L ∞ ( G , B ) of which the right translation is a continuous map from G into L ∞ ( G , B ) . Characterizations of the case where L RUC ( G , B ) is a Riesz ideal of L ∞ ( G , B ) are given in terms of the order-continuity of ∥ ∥ ∞ B on certain subspaces of L ∞ ( G ) . Throughout the paper, the discussion is carried out in...

Isometries between groups of invertible elements in Banach algebras

Osamu Hatori (2009)

Studia Mathematica

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We show that if T is an isometry (as metric spaces) from an open subgroup of the group of invertible elements in a unital semisimple commutative Banach algebra A onto a open subgroup of the group of invertible elements in a unital Banach algebra B, then T ( 1 ) - 1 T is an isometrical group isomorphism. In particular, T ( 1 ) - 1 T extends to an isometrical real algebra isomorphism from A onto B.

M -ideals of compact operators into ℓ p

Kamil John, Dirk Werner (2000)

Czechoslovak Mathematical Journal

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We show for 2 ≤ p < ∞ and subspaces X of quotients of L p with a 1 -unconditional finite-dimensional Schauder decomposition that K ( X , ℓ p ) is an M -ideal in L ( X , ℓ p ) .