scholarly journals Weighted Orlicz algebras on hypergroups

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 2991-3002
Author(s):  
Serap Öztop ◽  
Seyyed Tabatabaie
Keyword(s):  
Weight Function ◽  
Banach Algebra ◽  
Maximal Ideal ◽  
Approximate Identity ◽  
Ideal Space ◽  
Complementary Pair ◽  
Convolution Algebra ◽  
Algebraic Properties ◽  
Young Functions ◽  
Commutative Hypergroup

Let K be a hypergroup, w be a weight function and let (?,?) be a complementary pair of Young functions. We consider the weighted Orlicz space L??(K) and investigate some of its algebraic properties under convolution. We also study the existence of an approximate identity for the Banach algebra L?w(K). Further, we describe the maximal ideal space of the convolution algebra L?w(K) for a commutative hypergroup K.

scholarly journals The convolution algebraH1(R)

2010 ◽  
Vol 8 (2) ◽  
pp. 167-179 ◽  
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.

scholarly journals Tensor Products of Banach Algebras

1959 ◽  
Vol 11 ◽  
pp. 297-310 ◽  
Author(s):  
Bernard R. Gelbaum
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Banach Algebras ◽  
Cartesian Product ◽  
Commutative Banach Algebra ◽  
Maximal Ideal Space ◽  
Locally Compact Abelian Group ◽  
Ideal Space ◽  
Integrable Functions ◽  
Group A

This paper is concerned with a generalization of some recent theorems of Hausner (1) and Johnson (4; 5). Their result can be summarized as follows: Let G be a locally compact abelian group, A a commutative Banach algebra, B1 = Bl(G,A) the (commutative Banach) algebra of A-valued, Bochner integrable junctions on G, 3m1the maximal ideal space of A, m2the maximal ideal space of L1(G) [the [commutative Banach] algebra of complex-valued, Haar integrable functions on G, m3the maximal ideal space of B1. Then m3and the Cartesian product m1 X m2are homeomorphic when the spaces mi, i = 1, 2, 3, are given their weak* topologies. Furthermore, the association between m3and m1 X m2is such as to permit a description of any epimorphism E3: B1 → B1/m3 in terms of related epimorphisms E1: A → A/M1 and E2:L1(G) → Ll(G)/M2, where M1 is in mi i = 1, 2, 3.

scholarly journals Sectional representation of Banach modules and their multipliers

2003 ◽  
Vol 2003 (13) ◽  
pp. 817-825
Author(s):  
Terje Hõim ◽  
D. A. Robbins
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Commutative Banach Algebra ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Banach Module ◽  
The Past ◽  
Banach Modules ◽  
Quotient Modules

LetXbe a Banach module over the commutative Banach algebraAwith maximal ideal spaceΔ. We show that there is a norm-decreasing representation ofXas a space of bounded sections in a Banach bundleπ:ℰ→Δ, whose fibers are quotient modules ofX. There is also a representation ofM(X), the space of multipliersT:A→X, as a space of sections in the same bundle, but this representation may not be continuous. These sectional representations subsume results of various authors over the past three decades.

Boundaries For Real Banach Algebras

1976 ◽  
Vol 28 (1) ◽  
pp. 42-49 ◽  
Author(s):  
B. V. Limaye
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Banach Algebras ◽  
Maximal Ideal Space ◽  
Close Connection ◽  
Ideal Space ◽  
The Real ◽  
Šilov Boundary ◽  
The Absolute ◽  
Silov Boundary

Let A be a commutative real Banach algebra with unit, and MA its maximal ideal space. The existence of the Silov boundary SA for A was established in [5] by resorting to the complexification of A. We give here an intrinsic proof of this result which exhibits the close connection between the absolute values and the real parts of ‘functions’ in A (Theorem 1.3).

Analysis on Sparse Parts in the Maximal Ideal Space of H∞

1992 ◽  
Vol 44 (4) ◽  
pp. 805-823
Author(s):  
Keiji izuchi
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Analytic Functions ◽  
Level Sets ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Bounded Analytic Functions ◽  
Douglas Algebras

AbstractAnalysis on sparse parts of the Banach algebra of bounded analytic functions is given. It is proved that Sarason's theorem for QC-level sets cannot be generalized to general Douglas algebras.

scholarly journals REPRESENTATIONS OF REAL BANACH ALGEBRAS

2010 ◽  
Vol 88 (3) ◽  
pp. 289-300 ◽  
Author(s):  
F. ALBIAC ◽  
E. BRIEM
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Banach Algebras ◽  
Ideal Space ◽  
Gelfand Transform ◽  
Continuous Complex ◽  
Unital Banach Algebra ◽  
Complex Valued

AbstractA commutative complex unital Banach algebra can be represented as a space of continuous complex-valued functions on a compact Hausdorff space via the Gelfand transform. However, in general it is not possible to represent a commutative real unital Banach algebra as a space of continuous real-valued functions on some compact Hausdorff space, and for this to happen some additional conditions are needed. In this note we represent a commutative real Banach algebra on a part of its state space and show connections with representations on the maximal ideal space of the algebra (whose existence one has to prove first).

CENTRE OF BANACH ALGEBRA VALUED BEURLING ALGEBRAS

2021 ◽  
pp. 1-9
Author(s):  
BHARAT TALWAR ◽  
RANJANA JAIN
Keyword(s):  
Banach Algebra ◽  
Approximate Identity ◽  
Conjugacy Classes ◽  
Weak Amenability ◽  
Algebraic Properties ◽  
Formula Group ◽  
Beurling Algebras

Abstract We prove that for a Banach algebra A having a bounded $\mathcal {Z}(A)$ -approximate identity and for every $\mathbf {[IN]}$ group G with a weight w which is either constant on conjugacy classes or satisfies $w \geq 1$ , $\mathcal {Z}(L^{1}_{w}(G) \otimes ^{\gamma } A) \cong \mathcal {Z}(L^{1}_{w}(G)) \otimes ^{\gamma } \mathcal {Z}(A)$ . As an application, we discuss the conditions under which $\mathcal {Z}(L^{1}_{\omega }(G,A))$ enjoys certain Banach algebraic properties, such as weak amenability or semisimplicity.

scholarly journals On Lebesgue-type decompositions for Banach algebras

1970 ◽  
Vol 3 (1) ◽  
pp. 39-47
Author(s):  
Howard Anton
Keyword(s):  
Banach Algebra ◽  
Maximal Ideal ◽  
Borel Measure ◽  
Banach Algebras ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Borel Sets ◽  
Direct Sum ◽  
Gelfand Transform ◽  
Regular Borel Measure

If the maximal ideal space of a commutative complex unitary Banach algebra, X, is equipped with a nonnegative, finite, regular Borel measure, m, then for each element, x, in X, a. complex regular Borel measure, mx, can be obtained by integrating the Gelfand transform of x with respect to m over the Borel sets. This paper considers the possibility of direct sum decompositions of the form X = Ax ⊕ Px where Ax = {z ε X: mz ≪ mx} and Px = {z ε X: mz ┴ mx}.

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