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1
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Idempotents dans les algèbres de Banach

100%
Berkani M.
Studia Mathematica
|
1996
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tom 120
|
nr 2
155-158
EN
Using the holomorphic functional calculus we give a characterization of idempotent elements commuting with a given element in a Banach algebra.
2
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Continuity of the Drazin inverse II

80%
Koliha J., Rakočević V.
Studia Mathematica
|
1998
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tom 131
|
nr 2
167-177
EN
We study the continuity of the generalized Drazin inverse for elements of Banach algebras and bounded linear operators on Banach spaces. This work extends the results obtained by the second author on the conventional Drazin inverse.
3
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On the joint spectral radius

80%
Müller V.
Annales Polonici Mathematici
|
1997
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tom 66
|
nr 1
173-182
EN
We prove the $𝓁_p$-spectral radius formula for n-tuples of commuting Banach algebra elements
4
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Some remarks on the algebra of functions of two variables with bounded total \(\Phi\)-variation in Schramm sense

80%
Ereú T., Merentes N., Sánchez J. L.
Commentationes Mathematicae
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2010
|
tom 50
|
nr 1
EN
This paper is devoted to discuss some generalizations of the bounded total \(\Phi\)-variation in the sense of Schramm. This concept was defined by W. Schramm for functions of one real variable. In the paper we generalize the concept in question for the case of functions of of two variables defined on certain rectangle in the plane. The main result obtained in the paper asserts that the set of all functions having bounded total \(\Phi\)-variation in Schramm sense has the structure of a Banach algebra.
5
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An approach to joint spectra

80%
Meléndez A. M., Wawrzyńczyk A.
Annales Polonici Mathematici
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1999
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tom 72
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nr 2
131-144
EN
For a given unital Banach algebra A we describe joint spectra which satisfy the one-way spectral mapping property. Each spectrum of this class is uniquely determined by a family of linear subspaces of A called spectral subspaces. We introduce a topology in the space of all spectral subspaces of A and utilize it to the study of the properties of the spectra.
6
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Norm conditions for real-algebra isomorphisms between uniform algebras

80%
Shindo R.
Open Mathematics
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2010
|
tom 8
|
nr 1
135-147
EN
Let A and B be uniform algebras. Suppose that α ≠ 0 and A 1 ⊂ A. Let ρ, τ: A 1 → A and S, T: A 1 → B be mappings. Suppose that ρ(A 1), τ(A 1) and S(A 1), T(A 1) are closed under multiplications and contain expA and expB, respectively. If ‖S(f)T(g) − α‖∞ = ‖ρ(f)τ(g) − α‖∞ for all f, g ∈ A 1, S(e 1)−1 ∈ S(A 1) and S(e 1) ∈ T(A 1) for some e 1 ∈ A 1 with ρ(e 1) = 1, then there exists a real-algebra isomorphism $$ \tilde S $$: A → B such that $$ \tilde S $$(ρ(f)) = S(e 1)−1 S(f) for every f ∈ A 1. We also give some applications of this result.
7
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Perturbation theorems for Hermitian elements in Banach algebras

80%
Bhatia R., Drissi D.
Studia Mathematica
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1999
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tom 134
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nr 2
111-117
EN
Two well-known theorems for Hermitian elements in C*-algebras are extended to Banach algebras. The first concerns the solution of the equation ax - xb = y, and the second gives sharp bounds for the distance between spectra of a and b when a, b are Hermitian.
8
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Commutative, radical amenable Banach algebras

80%
Read C. J.
Studia Mathematica
|
2000
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tom 140
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nr 3
199-212
EN
There has been a considerable search for radical, amenable Banach algebras. Noncommutative examples were finally found by Volker Runde [R]; here we present the first commutative examples. Centrally placed within the construction, the reader may be pleased to notice a reprise of the undergraduate argument that shows that a normed space with totally bounded unit ball is finite-dimensional; we use the same idea (approximate the norm 1 vector x within distance η by a "good" vector $y_1$; then approximate $(x-y_1)/η$ within distance η by a "good" vector $y_2$, thus approximating x within distance $η^2$ by $y_1+η y_2$, and so on) to go from η=9/10 in Lemma 1.5 to arbitrarily small η in Lemma 2.1. This is not an arbitrary decision on the part of the author; it really is forced on him by the nature of the construction, see e.g. (6.1) for a place where η small at the start will not do.
9
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Closed operators affiliated with a Banach algebra of operators

70%
Barnes B. A.
Studia Mathematica
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1991-1992
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tom 101
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nr 3
215-240
EN
Let ℬ be a Banach algebra of bounded linear operators on a Banach space X. If S is a closed operator in X such that (λ - S)^{-1} ∈ ℬ for some number λ, then S is affiliated with ℬ. The object of this paper is to study the spectral theory and Fredholm theory relative to ℬ of an operator which is affiliated with ℬ. Also, applications are given to semigroups of operators which are contained in ℬ.
10
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Gelfand representation of Banach modules

62%
Kitchen J. W., Robbins D. A.
Instytut Matematyczny Polskiej Akademii Nauk
EN
Preface Let A be a commutative Banach algebra with maximal ideal space ∆ and let ^: A → C₀(∆) be the Gelfand representation of A. If M is a Banach module over A, then a bounded linear map φ: M → M₀, will be called a representation of M of Gelfund type if M₀ is a Banach module over C₀(∆) and φ is ^-linear in the sense that φ(ax) = âφ(x) for all a ∈ A and x ∈ M. Two such representations have been studied previously. In [50] and [51] Robbins describes such a representation in which M₀, is taken to be a space of continuous complex-valued functions. Varela and Hofmann have considered the special case in which A is a commutative C*-algebra with identity and in that case they describe a very different type of representation in which M₀ = Γ(π),the space of continuous sections of a bundle of Banach spaces π : E → ∆. The present paper generalizes considerably the sectional representation studied by Varela and Hofmann and shows its "equivalence" to the representation studied by Robbins. For a very large class of Banach modules (M, A), including essential modules over Banach algebras with bounded approximate identities, it is shown that there is a bundle of Banach spaces π : E → ∆ and a representation ^: M → Γ₀(π) which is not only of Gelfand type, but is universal with respect to all sectional representations of Gelfand type. This representation, which is unique up to isomorphism, is called the Gelfand representation of the module. Its basic properties are developed in the second section of the paper. Flanking this section are a preliminary section concerning bundles and a section devoted to examples. The final section explores functorially the relationships between Banach modules, bundles of Banach spaces, and their morphisms.
XX
CONTENTS Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. Bundles of Banach spaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2. Representations of Banach modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4. Functorial properties of the Gelfand representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Appendix. A correspondence between sections and complex-valued functions . . . . . . . . . . . . .42 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
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