Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Subalgebras of Douglas algebras
View through CrossRef
A closed subalgebra
A
\mathcal {A}
of
L
∞
{L^\infty }
is called a Douglas algebra in case
A
\mathcal {A}
is an algebra generated by
H
∞
{H^\infty }
and a set of inverses of inner functions. It is shown that if the Douglas algebra
A
\mathcal {A}
contains properly
H
∞
+
C
{H^\infty } + C
, then there is another Douglas algebra
A
′
\mathcal {A}’
such that
H
∞
+
C
⊊
A
′
⊊
A
{H^\infty } + C \subsetneq \mathcal {A}’ \subsetneq \mathcal {A}
. Some results on subalgebras are also given for algebras generated by
H
∞
{H^\infty }
and a function of the form
f
B
¯
f\overline B
, where
f
f
is in
H
∞
{H^\infty }
and
B
B
is an infinite Blaschke product.
American Mathematical Society (AMS)
Title: Subalgebras of Douglas algebras
Description:
A closed subalgebra
A
\mathcal {A}
of
L
∞
{L^\infty }
is called a Douglas algebra in case
A
\mathcal {A}
is an algebra generated by
H
∞
{H^\infty }
and a set of inverses of inner functions.
It is shown that if the Douglas algebra
A
\mathcal {A}
contains properly
H
∞
+
C
{H^\infty } + C
, then there is another Douglas algebra
A
′
\mathcal {A}’
such that
H
∞
+
C
⊊
A
′
⊊
A
{H^\infty } + C \subsetneq \mathcal {A}’ \subsetneq \mathcal {A}
.
Some results on subalgebras are also given for algebras generated by
H
∞
{H^\infty }
and a function of the form
f
B
¯
f\overline B
, where
f
f
is in
H
∞
{H^\infty }
and
B
B
is an infinite Blaschke product.
Related Results
Differential graded vertex Lie algebras
Differential graded vertex Lie algebras
This is the continuation of the study of differential graded (dg) vertex algebras defined in our previous paper [Caradot et al., “Differential graded vertex operator algebras and t...
WITHDRAWN: Roughness in L-algebras
WITHDRAWN: Roughness in L-algebras
Abstract
The aim of this paper is to introduce rough approximation on L−algebras. We investigate the relationship between subalgebras, ideals and rough subalgebras,...
Finitely Presented Heyting Algebras
Finitely Presented Heyting Algebras
In this paper we study the structure of finitely presented Heyting<br />algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every s...
Weak pseudo-BCK algebras
Weak pseudo-BCK algebras
Abstract
In this paper we define and study the weak pseudo-BCK algebras as generalizations of weak BCK-algebras, extending some results given by Cı⃖rulis for weak BC...
Malcev Yang-Baxter equation, weighted $\mathcal{O}$-operators on Malcev algebras and post-Malcev algebras
Malcev Yang-Baxter equation, weighted $\mathcal{O}$-operators on Malcev algebras and post-Malcev algebras
The purpose of this paper is to study the $\mathcal{O}$-operators on Malcev algebras and discuss the solutions of Malcev Yang-Baxter equation by $\mathcal{O}$-operators. Furthe...
Central invariants and enveloping algebras of braided Hom-Lie algebras
Central invariants and enveloping algebras of braided Hom-Lie algebras
Let (H,?) be a monoidal Hom-Hopf algebra and HH HYD the Hom-Yetter-Drinfeld
category over (H,?). Then in this paper, we first introduce the definition
of braided Hom-Lie alge...
On t-derivations of PMS-algebras
On t-derivations of PMS-algebras
Background PMS algebras are a type of algebraic structure that has been studied extensively in recent years. They are a generalization of several other algebraic structures, such a...
Pythagorean fuzzy LiuB – subalgebra of LiuB - algebra
Pythagorean fuzzy LiuB – subalgebra of LiuB - algebra
Background This article introduces the fuzzy LiuB-subalgebra (LBS) of LiuB-algebra (LBA), a concept previously undefined in the context of BCL-algebras (other than BCL+-algebras). ...