Generalized Analytic Fourier-Feynman Transform of Functionals in a Banach AlgebraℱA1,A2a,b

ON ALGEBRA ISOMORPHISMS BETWEEN p-BANACH BEURLING ALGEBRAS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972720001392 ◽

2021 ◽

pp. 1-12

Author(s):

PRAKASH A. DABHI ◽

DARSHANA B. LIKHADA

Keyword(s):

Banach Algebra ◽

Banach Algebras ◽

Discrete Groups ◽

Discrete Semigroups ◽

Beurling Algebras

Abstract Let $(G_1,\omega _1)$ and $(G_2,\omega _2)$ be weighted discrete groups and $0\lt p\leq 1$ . We characterise biseparating bicontinuous algebra isomorphisms on the p-Banach algebra $\ell ^p(G_1,\omega _1)$ . We also characterise bipositive and isometric algebra isomorphisms between the p-Banach algebras $\ell ^p(G_1,\omega _1)$ and $\ell ^p(G_2,\omega _2)$ and isometric algebra isomorphisms between $\ell ^p(S_1,\omega _1)$ and $\ell ^p(S_2,\omega _2)$ , where $(S_1,\omega _1)$ and $(S_2,\omega _2)$ are weighted discrete semigroups.

Download Full-text

A SPHERICAL VERSION OF THE KOWALSKI–SŁODKOWSKI THEOREM AND ITS APPLICATIONS

Journal of the Australian Mathematical Society ◽

10.1017/s1446788720000452 ◽

2020 ◽

pp. 1-26

Author(s):

SHIHO OI

Keyword(s):

Banach Algebra ◽

Function Space ◽

Affirmative Answer ◽

List Type ◽

Private Communication ◽

Type Number ◽

Uniform Algebras ◽

Surjective Isometry ◽

Complex Linear ◽

Local Map

Abstract Li et al. [‘Weak 2-local isometries on uniform algebras and Lipschitz algebras’, Publ. Mat.63 (2019), 241–264] generalized the Kowalski–Słodkowski theorem by establishing the following spherical variant: let A be a unital complex Banach algebra and let $\Delta : A \to \mathbb {C}$ be a mapping satisfying the following properties: (a) $\Delta $ is 1-homogeneous (that is, $\Delta (\lambda x)=\lambda \Delta (x)$ for all $x \in A$ , $\lambda \in \mathbb C$ ); (b) $\Delta (x)-\Delta (y) \in \mathbb {T}\sigma (x-y), \quad x,y \in A$ . Then $\Delta $ is linear and there exists $\lambda _{0} \in \mathbb {T}$ such that $\lambda _{0}\Delta $ is multiplicative. In this note we prove that if (a) is relaxed to $\Delta (0)=0$ , then $\Delta $ is complex-linear or conjugate-linear and $\overline {\Delta (\mathbf {1})}\Delta $ is multiplicative. We extend the Kowalski–Słodkowski theorem as a conclusion. As a corollary, we prove that every 2-local map in the set of all surjective isometries (without assuming linearity) on a certain function space is in fact a surjective isometry. This gives an affirmative answer to a problem on 2-local isometries posed by Molnár [‘On 2-local *-automorphisms and 2-local isometries of B(H)', J. Math. Anal. Appl.479(1) (2019), 569–580] and also in a private communication between Molnár and O. Hatori, 2018.

Download Full-text

Infinite-Dimensional Grassmann-Banach Algebra

Concise Encyclopedia of Supersymmetry ◽

10.1007/1-4020-4522-0_264 ◽

2004 ◽

pp. 201-201

Author(s):

John Howie ◽

Steven Duplij ◽

Ali Mostafazadeh ◽

Masaki Yasue ◽

Vladimir Ivashchuk

Keyword(s):

Banach Algebra ◽

Infinite Dimensional

Download Full-text

A characterization of Jordan and 5-Jordan homomorphisms between Banach algebras

Asian-European Journal of Mathematics ◽

10.1142/s1793557118500213 ◽

2018 ◽

Vol 11 (02) ◽

pp. 1850021 ◽

Cited By ~ 3

Author(s):

A. Zivari-Kazempour

Keyword(s):

Banach Algebra ◽

Banach Algebras ◽

Commutative Banach Algebra ◽

Jordan Homomorphism ◽

Jordan Homomorphisms ◽

Unital Banach Algebra

We prove that each surjective Jordan homomorphism from a Banach algebra [Formula: see text] onto a semiprime commutative Banach algebra [Formula: see text] is a homomorphism, and each 5-Jordan homomorphism from a unital Banach algebra [Formula: see text] into a semisimple commutative Banach algebra [Formula: see text] is a 5-homomorphism.

Download Full-text

Compact linear operators from an algebraic standpoint

Glasgow Mathematical Journal ◽

10.1017/s0017089500000069 ◽

1967 ◽

Vol 8 (1) ◽

pp. 41-49 ◽

Cited By ~ 4

Author(s):

F. F. Bonsall

Keyword(s):

Banach Algebra ◽

Banach Algebras ◽

Linear Operators ◽

Identity Operator ◽

Algebra Structure ◽

Natural Setting ◽

Norm Topology ◽

Bounded Linear ◽

Underlying Space ◽

Closed Subalgebra

Let B(X) denote the Banach algebra of all bounded linear operators on a Banach space X. Let t be an element of B(X), and let edenote the identity operator on X. Since the earliest days of the theory of Banach algebras, ithas been understood that the natural setting within which to study spectral properties of t is the Banach algebra B(X), or perhaps a closed subalgebra of B(X) containing t and e. The effective application of this method to a given class of operators depends upon first translating the data into terms involving only the Banach algebra structure of B(X) without reference to the underlying space X. In particular, the appropriate topology is the norm topology in B(X) given by the usual operator norm. Theorem 1 carries out this translation for the class of compact operators t. It is proved that if t is compact, then multiplication by t is a compact linear operator on the closed subalgebra of B(X) consisting of operators that commute with t.

Download Full-text

Closed Subalgebras of the Banach Algebra of Continuously Differentiable Functions on an Interval

Rocky Mountain Journal of Mathematics ◽

10.1216/rmjm/1181072972 ◽

1991 ◽

Vol 21 (2) ◽

pp. 829-855 ◽

Cited By ~ 1

Author(s):

Philip Downum ◽

J.A. Lindberg

Keyword(s):

Banach Algebra ◽

Differentiable Functions ◽

Closed Subalgebras

Download Full-text

The convolution algebraH1(R)

Journal of Function Spaces and Applications ◽

10.1155/2010/524036 ◽

2010 ◽

Vol 8 (2) ◽

pp. 167-179 ◽

Cited By ~ 3

Author(s):

R. L. Johnson ◽

C. R. Warner

Keyword(s):

Banach Algebra ◽

Maximal Ideal ◽

Tauberian Theorem ◽

Singular Integrals ◽

Approximate Identity ◽

Maximal Ideal Space ◽

Ideal Space

H1(R) is a Banach algebra which has better mapping properties under singular integrals thanL1(R) . We show that its approximate identity sequences are unbounded by constructing one unbounded approximate identity sequence {vn}. We introduce a Banach algebraQthat properly lies betweenH1andL1, and use it to show thatc(1 + lnn) ≤ ||vn||H1≤Cn1/2. We identify the maximal ideal space ofH1and give the appropriate version of Wiener's Tauberian theorem.

Download Full-text