scholarly journals On a class of vector-valued entire Dirichlet series in n variables

2018 ◽  
Vol 22 (1) ◽  
pp. 3-12 ◽  
Author(s):  
Lakshika Chutani ◽  
Niraj Kumar ◽  
Garima Manocha
Keyword(s):  
Banach Algebra ◽  
Dirichlet Series ◽  
Commutative Banach Algebra ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Entire Dirichlet Series ◽  
Vector Valued ◽  
Class F

We consider a class F of entire Dirichlet series in n variables, whose coefficients belong to a commutative Banach algebra E. With a well defined norm, F is proved to be a Banach algebra with identity. Further results on quasi-invertibility, spectrum and continuous linear functionals are proved for elements belonging to F.

scholarly journals Coefficient multipliers on spaces of vector-valued entire Dirichlet series

2017 ◽  
Vol 142 (3) ◽  
pp. 299-307
Author(s):  
Sharma Akanksha ◽  
Girja S. Srivastava
Keyword(s):  
Dirichlet Series ◽  
Entire Dirichlet Series ◽  
Vector Valued ◽  
Coefficient Multipliers

scholarly journals On continuity of derivations and epimorphisms on some vector-valued group algebras

1997 ◽  
Vol 56 (2) ◽  
pp. 209-215
Author(s):  
Ramesh V. Garimella
Keyword(s):  
Banach Algebra ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Group Algebras ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Zero Divisors ◽  
Integrable Functions ◽  
Vector Valued ◽  
Nontrivial Zero

For a locally compact Abelian group G and a commutative Banach algebra B, let L1(G, B) be the Banach algebra of all Bochner integrable functions. We show that if G is compact and B is a nonunital Banach algebra without nontrivial zero divisors, then (i) all derivations on L1(G, B) are continuous if and only if all derivations on B are continuous, and (ii) each epimorphism from a Banach algebra X onto L1(G, B) is continuous provided every epimorphism from X onto B is continuous. If G is noncompact then every derivation on L1(G, B) and every epimorphism from a commutative Banach algebra onto L1(G, B) are continuous. Our results extend the results of Neumann and Velasco for nonunital Banach algebras.

scholarly journals Higher point derivations on commutative Banach algebras, III

1981 ◽  
Vol 24 (1) ◽  
pp. 31-40 ◽  
Author(s):  
H. G. Dales ◽  
J. P. McClure
Keyword(s):  
Banach Algebra ◽  
Infinite Order ◽  
Infinite Sequence ◽  
Banach Algebras ◽  
Commutative Banach Algebra ◽  
Complex Field ◽  
Linear Functionals ◽  
Point Derivation ◽  
Commutative Banach Algebras ◽  
Image Position

Let A be a commutative Banach algebra with identity 1 over the complex field C, and let d0 be a character on A. We recall that a (higher) point derivation of order q on A at d0 is a sequence d1, …, dq of linear functionals on A such that the identitieshold for each choice of f and g in A and k in {1, …, q}. A point derivation of infinite order is an infinite sequence {dk} of linear functionals such that (1.1) holds for all k. A point derivation is continuous if each dk is continuous, totally discontinuous if dk is discontinuous for each k≧1, and degenerate if d1 = 0.

scholarly journals On Vector Valued Multipliers for the Class of Strongly ℋ𝒦-Integrable Functions

2017 ◽  
Vol 68 (1) ◽  
pp. 69-79
Author(s):  
Surinder Pal Singh ◽  
Savita Bhatnagar
Keyword(s):  
Banach Algebra ◽  
Bounded Variation ◽  
Multiplication Operator ◽  
Commutative Banach Algebra ◽  
Partial Converse ◽  
Integrable Functions ◽  
Vector Valued

Abstract We investigate the space of vector valued multipliers of strongly Henstock-Kurzweil integrable functions. We prove that if X is a commutative Banach algebra with identity e such that ‖e‖ = 1 and g : [a, b] → X is of strongly bounded variation, then the multiplication operator defined by Mg(f) := fg maps 𝒮ℋ𝒦 to ℋ𝒦. We also prove a partial converse, when X is a Gel’fand space.

Representation of Linear Functionals on Köthe Spaces

1953 ◽  
Vol 5 ◽  
pp. 568-575 ◽  
Author(s):  
G. G. Lorentz ◽  
D. G. Wertheim
Keyword(s):  
Banach Space ◽  
Linear Functional ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Continuous Linear Functional ◽  
Köthe Spaces ◽  
Integrable Functions ◽  
Köthe Space ◽  
Vector Valued

Kothe spaces, in the terminology of Diendonné [2], are certain spaces X of real valued integrable functions. In this paper we consider the problem of representation of continuous linear functional on vector valued Kothe spaces. The elements of a Kôthe space X(B) are functions with values in a Banach space B (see §2).

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 Extending Edgar's ordering to locally convex spaces

1992 ◽  
Vol 34 (2) ◽  
pp. 175-188
Author(s):  
Neill Robertson
Keyword(s):  
Convex Space ◽  
Dual Pair ◽  
Locally Convex Space ◽  
Vector Spaces ◽  
Locally Convex Spaces ◽  
Continuous Linear ◽  
Linear Functionals ◽  
Hausdorff Topological Vector Space ◽  
Locally Convex ◽  
Mackey Topologies

By the term “locally convex space”, we mean a locally convex Hausdorff topological vector space (see [17]). We shall denote the algebraic dual of a locally convex space E by E*, and its topological dual by E′. It is convenient to think of the elements of E as being linear functionals on E′, so that E can be identified with a subspace of E′*. The adjoint of a continuous linear map T:E→F will be denoted by T′:F′→E′. If 〈E, F〈 is a dual pair of vector spaces, then we shall denote the corresponding weak, strong and Mackey topologies on E by α(E, F), β(E, F) and μ(E, F) respectively.

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