The maximal ideal space of bounded, analytic, dirichlet finite functions

1978 ◽  
Vol 31 (1) ◽  
pp. 298-301 ◽  
Author(s):  
Kwang-nan Chow ◽  
David Protas
Keyword(s):  
Maximal Ideal ◽  
Maximal Ideal Space ◽  
Ideal Space

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.

The Maximal Ideal Space of Subalgebras of the Disk Algebra

1975 ◽  
Vol 18 (1) ◽  
pp. 61-65 ◽  
Author(s):  
Bruce Lund
Keyword(s):  
Unit Disk ◽  
Maximal Ideal ◽  
Function Algebra ◽  
Continuous Functions ◽  
Maximal Ideal Space ◽  
Open Unit ◽  
Ideal Space ◽  
Disk Algebra ◽  
Closed Subalgebra ◽  
Uniformly Closed

Let X be a compact Hausdorff space and C(X) the complexvalued continuous functions on X. We say A is a function algebra on X if A is a point separating, uniformly closed subalgebra of C(X) containing the constant functions. Equipped with the sup-norm ‖f‖ = sup{|f(x)|: x ∊ X} for f ∊ A, A is a Banach algebra. Let MA denote the maximal ideal space.Let D be the closed unit disk in C and let U be the open unit disk. We call A(D)={f ∊ C(D):f is analytic on U} the disk algebra. Let T be the unit circle and set C1(T) = {f ∊ C(T): f'(t) ∊ C(T)}.

Homeomorphic Analytic Maps into the Maximal Ideal Space of H∞

1999 ◽  
Vol 51 (1) ◽  
pp. 147-163 ◽  
Author(s):  
Daniel Suárez
Keyword(s):  
Maximal Ideal ◽  
Maximal Ideal Space ◽  
Ideal Space ◽  
Gleason Part ◽  
Interpolating Sequences ◽  
Closed Subalgebra ◽  
Analytic Maps ◽  
The Ideal

AbstractLet m be a point of the maximal ideal space of H∞ with nontrivial Gleason part P(m). If Lm : D → P(m) is the Hoffman map, we show that H∞ ° Lm is a closed subalgebra of H∞. We characterize the points m for which Lm is a homeomorphism in terms of interpolating sequences, and we show that in this case H∞ ° Lm coincides with H∞. Also, if Im is the ideal of functions in H∞ that identically vanish on P(m), we estimate the distance of any f ϵ H∞ to Im.

The Maximal Ideal Space of H∞ + C on the ball in Cn

1979 ◽  
Vol 31 (1) ◽  
pp. 79-86 ◽  
Author(s):  
Gerard Mcdonald
Keyword(s):  
Maximal Ideal ◽  
Banach Algebras ◽  
Holomorphic Functions ◽  
Maximal Ideal Space ◽  
Open Unit ◽  
Ideal Space ◽  
Open Unit Ball ◽  
Closed Subalgebra ◽  
Image Position ◽  
Bounded Holomorphic

Let S denote the unit sphere in Cn, B the (open) unit ball in Cn and H∞(B) the collection of all bounded holomorphic functions on B. For f ∈ H∞(B) the limitsexist for almost every ζ in S, and the map ƒ → ƒ* defines an isometric isomorphism from H∞(B) onto a closed subalgebra of L∞(S), denoted H∞(S). (The only measure on S we will refer to in this paper is the Lebesgue measure, dσ, generated by Euclidean surface area.) Rudin has shown in [4] that the spaces H∞(B) + C(B) and H∞(S) + C(S) are Banach algebras in the sup norm. In this paper we will show that the maximal ideal space of H∞(B) + C(B), Σ (H∞(B) + C(B)), is naturally homeomorphic to Σ (H∞(B)) and that Z (H∞(S) + C(S)) is naturally homeomorphic to Σ (H∞(S))\B.

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