Closed Subalgebras of Homogeneous Banach Algebras

2020 ◽  
pp. 142-161
Author(s):  
Hwai-chiuan Wang
Keyword(s):  
Banach Algebras ◽  
Closed Subalgebras

scholarly journals A characterisation of closed subalgebras of

1977 ◽  
Vol 20 (3) ◽  
pp. 215-217 ◽  
Author(s):  
P. G. Dixon
Keyword(s):  
Banach Algebras ◽  
Closed Subalgebras

We show that the class of Banach algebras A isomorphic with normclosed (non-self-adjoint) subalgebras of is characterized by the condition that the norms of polynomials in A be dominated by the norms of the same polynomials in .

scholarly journals Closed subalgebras of homogeneous Banach algebras

1975 ◽  
Vol 20 (3) ◽  
pp. 366-376 ◽  
Author(s):  
Ching-Nan Tseng ◽  
Hawi-Chiuan Wang
Keyword(s):  
Abelian Group ◽  
Compact Abelian Group ◽  
Banach Algebras ◽  
Synthesis Method ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Necessary And Sufficient ◽  
Closed Subalgebras ◽  
Segal Algebras

AbstractRudin's synthesis method for investigating closed subalgebras of L1(G), where G is an infinite compact abelian group, is extended to the study of closed subalgebras in homogeneous Banach algebras and Segal algebras. Necessary and sufficient conditions are given for the synthesis to hold in certain classes of homogeneous Banach algebras and it is proved that in the Ap(G) algebras the synthesis holds for 1 ≦ p 2 but fails for Ap(T), 2 < p < ∞.

scholarly journals Rudin synthesis on homogeneous Banach algebras

1980 ◽  
Vol 29 (4) ◽  
pp. 407-416
Author(s):  
Rong-Song Jih ◽  
Hwai-Chiuan Wang
Keyword(s):  
Banach Algebra ◽  
Necessary Conditions ◽  
Banach Algebras ◽  
Closed Ideal ◽  
Closed Subalgebra ◽  
Sufficient And Necessary Conditions ◽  
Definition Of ◽  
Closed Subalgebras

AbstractThe main results of this article are (I) Let B be a homogeneous Banach algebra, A a closed subalgebra of B, and I the largest closed ideal of B contained in A. We assert that for some closed subalgebra J of B. Furthermore, under suitable conditions, we show that A is an R-subalgebra if and only if J is an R-subalgebra. A number of concrete closed subalgebras of a homogeneous Banach algebra therefore are R-subalgebras. For the definition of P(A) and that of an R-subalgebra, see the introduction in Section 1. (II) We give sufficient and necessary conditions for a closed subalgebra of Lp(G), 1 ≦ p ≦ ∞, to be an R-subalgebra.

Solvability of a 2 x 2 block operator matrix of chandrasekhar type on a Bananch algebra

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5169-5175 ◽  
Author(s):  
H.H.G. Hashem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence Of Solutions ◽  
Banach Algebras ◽  
Operator Matrix ◽  
Nonlinear Operators ◽  
Block Operator Matrix ◽  
Block Operator ◽  
Quadratic Integral ◽  
Quadratic Integral Equations

In this paper, we study the existence of solutions for a system of quadratic integral equations of Chandrasekhar type by applying fixed point theorem of a 2 x 2 block operator matrix defined on a nonempty bounded closed convex subsets of Banach algebras where the entries are nonlinear operators.

scholarly journals COMMUTATIVITY UP TO A FACTOR IN BANACH ALGEBRAS

2005 ◽  
Vol 38 (4) ◽  
pp. 895-900
Author(s):  
Christoph Schmoeger
Keyword(s):  
Banach Algebras

ON ALGEBRA ISOMORPHISMS BETWEEN p-BANACH BEURLING ALGEBRAS

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.

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