Gelfand transform for a Boehmian space of analytic functions

V. Karunakaran, and R. Angeline Chella Rajathi. "Gelfand transform for a Boehmian space of analytic functions." Annales Polonici Mathematici 101.1 (2011): 39-45. <http://eudml.org/doc/280994>.

@article{V2011,
abstract = {Let $H^∞()$ denote the usual commutative Banach algebra of bounded analytic functions on the open unit disc of the finite complex plane, under Hadamard product of power series. We construct a Boehmian space which includes the Banach algebra A where A is the commutative Banach algebra with unit containing $H^∞()$. The Gelfand transform theory is extended to this setup along with the usual classical properties. The image is also a Boehmian space which includes the Banach algebra C(Δ) of continuous functions on the maximal ideal space Δ (where Δ is given the usual Gelfand topology). It is shown that every F ∈ C(Δ) is the Gelfand transform of a suitable Boehmian. It should be noted that in the classical theory the Gelfand transform from A into C(Δ) is not surjective even though it can be shown that the image is dense. Thus the context of Boehmians enables us to identify every element of C(Δ) as the Gelfand transform of a suitable convolution quotient of analytic functions. (Here the convolution is the Hadamard convolution).},
author = {V. Karunakaran, R. Angeline Chella Rajathi},
journal = {Annales Polonici Mathematici},
keywords = {Banach algebra; Hadamard convolution; Boehmian space; Gelfand transform},
language = {eng},
number = {1},
pages = {39-45},
title = {Gelfand transform for a Boehmian space of analytic functions},
url = {http://eudml.org/doc/280994},
volume = {101},
year = {2011},
}

TY - JOUR
AU - V. Karunakaran
AU - R. Angeline Chella Rajathi
TI - Gelfand transform for a Boehmian space of analytic functions
JO - Annales Polonici Mathematici
PY - 2011
VL - 101
IS - 1
SP - 39
EP - 45
AB - Let $H^∞()$ denote the usual commutative Banach algebra of bounded analytic functions on the open unit disc of the finite complex plane, under Hadamard product of power series. We construct a Boehmian space which includes the Banach algebra A where A is the commutative Banach algebra with unit containing $H^∞()$. The Gelfand transform theory is extended to this setup along with the usual classical properties. The image is also a Boehmian space which includes the Banach algebra C(Δ) of continuous functions on the maximal ideal space Δ (where Δ is given the usual Gelfand topology). It is shown that every F ∈ C(Δ) is the Gelfand transform of a suitable Boehmian. It should be noted that in the classical theory the Gelfand transform from A into C(Δ) is not surjective even though it can be shown that the image is dense. Thus the context of Boehmians enables us to identify every element of C(Δ) as the Gelfand transform of a suitable convolution quotient of analytic functions. (Here the convolution is the Hadamard convolution).
LA - eng
KW - Banach algebra; Hadamard convolution; Boehmian space; Gelfand transform
UR - http://eudml.org/doc/280994
ER -