Hermitian Operators and Isometries on Banach Algebras of Continuous Maps with Values in Unital Commutative <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>-Algebras

Hatori, Osamu

doi:10.1155/2018/8085304

Cited by 6 publications

(10 citation statements)

References 38 publications

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“…Corollary 2 (Corollary 2 [13]). Let A and B be unital semisimple commutative Banach algebras with natural norms.…”

Section: A Theorem Of Jarosz On Isometries Which Preservementioning

confidence: 96%

“…We provide a precise proof of a theorem of Jarosz in [13] by making an ambitious revision of one in [18].…”

Section: A Theorem Of Jarosz On Isometries Which Preservementioning

confidence: 99%

“…The main result Theorem 14 in [13] with a detailed proof is recaptured as Theorem 9 in this paper. It gives the form of a surjective isometry U between certain Banach algebra of continuous maps with values in unital C * -algebras.…”

Section: Introductionmentioning

confidence: 97%

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Isometries on Banach algebras of $C(Y)$-valued maps

Hatori¹

2018

Preprint

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“…Corollary 2 (Corollary 2 [13]). Let A and B be unital semisimple commutative Banach algebras with natural norms.…”

Section: A Theorem Of Jarosz On Isometries Which Preservementioning

confidence: 96%

“…We provide a precise proof of a theorem of Jarosz in [13] by making an ambitious revision of one in [18].…”

Section: A Theorem Of Jarosz On Isometries Which Preservementioning

confidence: 99%

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Isometries on Banach algebras of $C(Y)$-valued maps

Hatori¹

2018

Preprint

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“…Surjective linear isometries of Lip([0, 1]), with both the σ-norm or the m-norm, were characterized as a sum of a weighted composition operator and an integral operator by Koshimizu [1,2], in contrast with the isometry groups of Lip([0, 1]), with both the Σ-norm or the M-norm, whose members have a canonical form in the sense that they can be represented as a weighted composition operator [3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Algebraic Reflexivity of Non-Canonical Isometries on Lipschitz Spaces

Jiménez-Vargas

Ramírez

2021

Mathematics

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Let Lip([0,1]) be the Banach space of all Lipschitz complex-valued functions f on [0,1], equipped with one of the norms: fσ=|f(0)|+f′L∞ or fm=max|f(0)|,f′L∞, where ·L∞ denotes the essential supremum norm. It is known that the surjective linear isometries of such spaces are integral operators, rather than the more familiar weighted composition operators. In this paper, we describe the topological reflexive closure of the isometry group of Lip([0,1]). Namely, we prove that every approximate local isometry of Lip([0,1]) can be represented as a sum of an elementary weighted composition operator and an integral operator. This description allows us to establish the algebraic reflexivity of the sets of surjective linear isometries, isometric reflections, and generalized bi-circular projections of Lip([0,1]). Additionally, some complete characterizations of such reflections and projections are stated.

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“…Surjective isometries (not necessarily linear) between spaces of vector-valued absolutely continuous functions with values in a strictly convex normed space have been studied in [11]. In the recent paper [10] of Hatori, he studies linear isometries between certain Banach algebras with values in C(Y ), where Y is a compact Hausdorff space. These Banach algebras include the C(Y )-valued Banach algebra of Lipschitz functions and C(Y )valued Banach algebra of continuously differentiable functions.…”

Section: Introductionmentioning

confidence: 99%

Isometries between completely regular vector-valued function spaces

Mojahedi¹,

Sady²

2020

Preprint

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In this paper, first we study surjective isometries (not necessarily linear) between completely regular subspaces A and B of C 0 (X, E) and C 0 (Y, F ) where X and Y are locally compact Hausdorff spaces and E and F are normed spaces, not assumed to be neither strictly convex nor complete. We show that for a class of normed spaces F satisfying a new defined property related to their T -sets, such an isometry is a (generalized) weighted composition operator up to a translation. Then we apply the result to study surjective isometries between A and B whenever A and B are equipped with certain norms rather than the supremum norm. Our results unify and generalize some recent results in this context.

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Hermitian Operators and Isometries on Banach Algebras of Continuous Maps with Values in Unital Commutative C⁎-Algebras

Abstract: We study isometries on algebras of the Lipschitz maps and the continuously differentiable maps with the values in a commutative unital C⁎-algebra. A precise proof of a theorem of Jarosz concerning isometries on spaces of continuous functions is exhibited.

Cited by 6 publications

References 38 publications

Isometries on Banach algebras of $C(Y)$-valued maps

Isometries on Banach algebras of $C(Y)$-valued maps

Algebraic Reflexivity of Non-Canonical Isometries on Lipschitz Spaces

Isometries between completely regular vector-valued function spaces

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