Two results on very strongly homogeneous algebras

1970 ◽  
Vol 68 (2) ◽  
pp. 363-376
Author(s):  
T. W. Körner
Keyword(s):  
Banach Algebra ◽  
Analytic Functions ◽  
Carrier Space ◽  
Homogeneous Algebras ◽  
Homogeneous Algebra

AbstractWe show that under quite general circumstances a Banach algebra R need not be closed in its tilda algebra . In answer to a query of Katznelson we show that there is a very strongly homogeneous algebra B ≠ C0(R) on R with R as carrier space such that non-analytic functions operate on B.

scholarly journals Analytic functions which operate on homogeneous algebras

1988 ◽  
Vol 45 (1) ◽  
pp. 1-10
Author(s):  
J. A. Ward
Keyword(s):  
Fixed Point ◽  
Compact Group ◽  
Banach Algebra ◽  
Analytic Functions ◽  
Operator Algebras ◽  
Commutative Banach Algebra ◽  
Open Set ◽  
Homogeneous Algebras ◽  
Complex Valued

AbstractIt is well known that a complex-valued function ø, analytic on some open set Ω, extends to any commutative Banach algebra B so that the action of ø on B commutes with the action of the Gelfand transformation. In this paper, it is shown that if B is a homogeneous convolution Banach algebra over any compact group and if 0 ∈ Ω is a fixed point of ø, then a similar result holds, with the Gelfand transformation replaced by the Fourier-Stieltjes transformation. Care is required, in that discussion of this relation usually requires simultaneous consideration of the extension of ø to B and to certain operator algebras.

LIPSCHITZ-TYPE INEQUALITIES FOR ANALYTIC FUNCTIONS IN BANACH ALGEBRAS

2019 ◽  
Vol 100 (3) ◽  
pp. 489-497
Author(s):  
SILVESTRU SEVER DRAGOMIR
Keyword(s):  
Analytic Function ◽  
Banach Algebra ◽  
Analytic Functions ◽  
Banach Algebras ◽  
Logarithmic Functions

In this paper we provide some bounds for the quantity $\Vert f(y)-f(x)\Vert$, where $f:D\rightarrow \mathbb{C}$ is an analytic function on the domain $D\subset \mathbb{C}$ and $x$, $y\in {\mathcal{B}}$, a Banach algebra, with the spectra $\unicode[STIX]{x1D70E}(x)$, $\unicode[STIX]{x1D70E}(y)\subset D$. Applications for the exponential and logarithmic functions on the Banach algebra ${\mathcal{B}}$ are also given.

scholarly journals A decomposition theorem for homogeneous algebras

2002 ◽  
Vol 72 (1) ◽  
pp. 47-56 ◽  
Author(s):  
L. G. Sweet ◽  
J. A. Macdougall
Keyword(s):  
Nonzero Element ◽  
Decomposition Theorem ◽  
Small Dimension ◽  
Infinite Field ◽  
Left Multiplication ◽  
One Dimensional ◽  
Direct Sum ◽  
Homogeneous Algebras ◽  
The One ◽  
Homogeneous Algebra

AbstractAn algebra A is homogeneous if the automorphism group of A acts transitively on the one dimensional subspaces of A. Suppose A is a homogeneous algebra over an infinite field k. Let La denote left multiplication by any nonzero element a ∈ A. Several results are proved concerning the structure of A in terms of La. In particular, it is shown that A decomposes as the direct sum A = ker La Im La. These results are then successfully applied to the problem of classifying the infinite homogeneous algebras of small dimension.

scholarly journals Homogeneous algebras on the circle. I. Ideals of analytic functions

1972 ◽  
Vol 22 (3) ◽  
pp. 1-19 ◽  
Author(s):  
Colin Bennett ◽  
John E. Gilbert
Keyword(s):  
Analytic Functions ◽  
Homogeneous Algebras

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.

Analytic Functions of Several Banach Algebra Elements

1955 ◽  
Vol 62 (2) ◽  
pp. 204 ◽  
Author(s):  
Richard Arens ◽  
A. P. Calderon
Keyword(s):  
Banach Algebra ◽  
Analytic Functions

scholarly journals Validity of Closed Ideals in Algebras of Series of Square Analytic Functions

2021 ◽  
Vol 5 (1) ◽  
pp. p20
Author(s):  
Musa Siddig ◽  
Shawgy Hussein ◽  
Amani Elseid
Keyword(s):  
Banach Algebra ◽  
Unit Disk ◽  
Analytic Functions ◽  
Dirichlet Space ◽  
Commutative Banach Algebra ◽  
Square Functions

We show the validity of a complete description of closed ideals of the algebra which is a commutative Banach algebra , that endowed with a pointwise operations act on Dirichlet space of algebra of series of analytic functions on the unit disk  satisfying the Lipscitz condition of order of square sequence  obtained by (Brahim Bouya, 2008), we introduce and deal with approximation square functions which is an outer functions to produce and show results in .

scholarly journals On approximation of homomorphisms of algebras of entire functions on Banach spaces

2019 ◽  
Vol 11 (1) ◽  
pp. 158-162
Author(s):  
H.M. Pryimak
Keyword(s):  
Banach Space ◽  
Unit Ball ◽  
Banach Algebra ◽  
Banach Spaces ◽  
Analytic Functions ◽  
Entire Functions ◽  
Commutative Banach Algebra ◽  
Uniformly Continuous ◽  
Positive Results

It is known due to R. Aron, B. Cole and T. Gamelin that every complex homomorphism of the algebra of entire functions of bounded type on a Banach space $X$ can be approximated in some sense by a net of point valued homomorphism. In this paper we consider the question about a generalization of this result for the case of homomorphisms to any commutative Banach algebra $A.$ We obtained some positive results if $A$ is the algebra of uniformly continuous analytic functions on the unit ball of $X.$

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