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 $X.$

scholarly journals Approximation by invertible functions of $H^{\infty}$

2006 ◽  
Vol 99 (2) ◽  
pp. 287 ◽  
Author(s):  
Artur Nicolau ◽  
Daniel Suárez
Keyword(s):  
Banach Algebra ◽  
Unit Disk ◽  
Analytic Functions ◽  
Banach Algebras ◽  
Bounded Analytic Functions ◽  
Analytic Proof ◽  
Dense Image

We provide an analytic proof that if $H^\infty$ is the algebra of bounded analytic functions on the unit disk, $A$ is a Banach algebra and $f: H^\infty \rightarrow A$ is a Banach algebras morphism with dense image, then $f((H^\infty)^{-1})$ is dense in $A^{-1}$.

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.

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 Difference formula defined by a new differential symmetric operator for a class of meromorphically multivalent functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Ibtisam Aldawish
Keyword(s):  
Differential Operator ◽  
Boundary Value Problems ◽  
Unit Disk ◽  
Spectral Theory ◽  
Analytic Functions ◽  
Special Class ◽  
Symmetric Operator ◽  
New Class ◽  
Difference Formula ◽  
Symmetric Operators

AbstractSymmetric operators have benefited in different fields not only in mathematics but also in other sciences. They appeared in the studies of boundary value problems and spectral theory. In this note, we present a new symmetric differential operator associated with a special class of meromorphically multivalent functions in the punctured unit disk. This study explores some of its geometric properties. We consider a new class of analytic functions employing the suggested symmetric differential operator.

scholarly journals QKtype spaces of analytic functions

2006 ◽  
Vol 4 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Hasi Wulan ◽  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Nondecreasing Function ◽  
Necessary And Sufficient Conditions ◽  
Type Space ◽  
Necessary And Sufficient ◽  
Spaces Of Analytic Functions

For a nondecreasing functionK:[0,8)?[0,8)and0<p<8,-2<q<8, we introduceQK(p,q), aQKtype space of functions analytic in the unit disk and study the characterizations ofQK(p,q). Necessary and sufficient conditions onKsuch thatQK(p,q)become some known spaces are given.

scholarly journals Partial sums of certain analytic functions

2001 ◽  
Vol 25 (12) ◽  
pp. 771-775 ◽  
Author(s):  
Shigeyoshi Owa
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Partial Sums ◽  
Open Unit ◽  
Open Unit Disk

The object of the present paper is to consider the starlikeness and convexity of partial sums of certain analytic functions in the open unit disk.

scholarly journals On the univalency for certain subclass of analytic functions involving Ruscheweyh derivatives

2002 ◽  
Vol 31 (9) ◽  
pp. 567-575 ◽  
Author(s):  
Liu Mingsheng
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Covering Theorem ◽  
Inclusion Relations ◽  
Special Case ◽  
Class Of Functions

LetHbe the class of functionsf(z)of the formf(z)=z+∑ K=2 + ∞a k z k, which are analytic in the unit diskU={z;|z|<1}. In this paper, we introduce a new subclassBλ(μ,α,ρ)ofHand study its inclusion relations, the condition of univalency, and covering theorem. The results obtained include the related results of some authors as their special case. We also get some new results.

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