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.

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 $X.$

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 Compact group actions on operator algebras and their spectra

2020 ◽  
Vol 126 (2) ◽  
pp. 276-292
Author(s):  
Costel Peligrad
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Compact Group ◽  
Spectral Properties ◽  
Operator Algebras ◽  
Abelian Groups ◽  
Group Actions ◽  
Algebraic Properties

We consider a class of dynamical systems with compact non-abelian groups that include C*-, W*- and multiplier dynamical systems. We prove results that relate the algebraic properties such as simplicity or primeness of the fixed point algebras to the spectral properties of the action, including the Connes and strong Connes spectra.

scholarly journals Spatial numerical ranges of elements of subalgebras ofC0(X)

2000 ◽  
Vol 23 (12) ◽  
pp. 827-831
Author(s):  
Sin-Ei Takahasi
Keyword(s):  
Banach Algebra ◽  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Numerical Range ◽  
Commutative Banach Algebra ◽  
Locally Compact ◽  
Continuous Complex ◽  
Complex Valued ◽  
Locally Compact Hausdorff Space

WhenAis a subalgebra of the commutative Banach algebraC0(X)of all continuous complex-valued functions on a locally compact Hausdorff spaceX, the spatial numerical range of element ofAcan be described in terms of positive measures.

Approximation of Piecewise Continuous Functions by Quotients of Bounded Analytic Functions

1972 ◽  
Vol 24 (4) ◽  
pp. 642-657 ◽  
Author(s):  
Donald Sarason
Keyword(s):  
Banach Algebra ◽  
Analytic Functions ◽  
Fourier Coefficients ◽  
Continuous Functions ◽  
Affirmative Answer ◽  
Bounded Analytic Functions ◽  
Closed Subalgebra ◽  
Boundary Functions ◽  
Piecewise Continuous ◽  
Complex Valued

This paper concerns a certain subalgebra of the Banach algebra of complex valued, essentially bounded, Lebesgue measurable functions on the unit circle in the complex plane (denoted here by L∞). My interest in this subalgebra was prompted by a question of R. G. Douglas. Let H∞ denote the space of functions in L∞ whose Fourier coefficients with negative indices vanish (equivalently, the space of boundary functions for bounded analytic functions in the unit disk). Douglas [5] has asked whether every closed subalgebra of L∞ containing H∞ is determined by the functions in H∞ that it makes invertible. More precisely, is such an algebra generated by H∞ and the inverses of the functions in H∞ that are invertible in the algebra? An affirmative answer is known for L∞ itself and for certain subalgebras of L∞ recently studied by Davie, Gamelin, and Garnett [3]. At the time of this writing, no algebra is known for which the above question can be answered negatively.

scholarly journals Duality for compact group actions on operator algebras and applications: Irreducible inclusions and Galois correspondence

2020 ◽  
Vol 31 (09) ◽  
pp. 2050067
Author(s):  
Costel Peligrad
Keyword(s):  
Fixed Point ◽  
Compact Group ◽  
Operator Algebras ◽  
Group Actions ◽  
Normal Subgroups ◽  
Galois Correspondence ◽  
Duality Property ◽  
Relative Commutant ◽  
Fixed Point Algebra

We consider compact group actions on C*- and W*-algebras. We prove results that relate the duality property of the action (as defined in the Introduction) with other relevant properties of the system such as the relative commutant of the fixed point algebras being trivial (called the irreducibility of the inclusion) and also to the Galois correspondence between invariant C*-subalgebras containing the fixed point algebra and the class of closed normal subgroups of the compact group.

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

2018 ◽  
Vol 11 (02) ◽  
pp. 1850021 ◽  
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.

scholarly journals Some Common Fixed-Point Theorems for Generalized-Contractive-Type Mappings on Complex-Valued Metric Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Chakkrid Klin-eam ◽  
Cholatis Suanoom
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Type ◽  
Complex Valued ◽  
Common Fixed Point Theorems

Fixed-point theory in complex valued metric spaces has greatly developed in recent times. In this paper, we prove certain common fixed-point theorems for two single-valued mappings in such spaces. The mappings we consider here are assumed to satisfy certain metric inequalities with generalized fixed-point theorems due to Rouzkard and Imdad (2012). This extends and subsumes many results of other authors which were obtained for mappings on complex-valued metric spaces.

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