Topological algebras with pseudoconvexly bounded elements

Mati Abel

Banach Center Publications (2005)

  • Volume: 67, Issue: 1, page 21-33
  • ISSN: 0137-6934

Abstract

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It is shown that every commutative sequentially bornologically complete Hausdorff algebra A with bounded elements is representable in the form of an (algebraic) inductive limit of an inductive system of locally bounded Fréchet algebras with continuous monomorphisms if the von Neumann bornology of A is pseudoconvex. Several classes of topological algebras A for which r A ( a ) ≤ β A ( a ) or r A ( a ) = β A ( a ) for each a ∈ A are described.

How to cite

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Mati Abel. "Topological algebras with pseudoconvexly bounded elements." Banach Center Publications 67.1 (2005): 21-33. <http://eudml.org/doc/281651>.

@article{MatiAbel2005,
abstract = {It is shown that every commutative sequentially bornologically complete Hausdorff algebra A with bounded elements is representable in the form of an (algebraic) inductive limit of an inductive system of locally bounded Fréchet algebras with continuous monomorphisms if the von Neumann bornology of A is pseudoconvex. Several classes of topological algebras A for which $r_A(a) ≤ β_A(a)$ or $r_A(a) = β_A(a)$ for each a ∈ A are described.},
author = {Mati Abel},
journal = {Banach Center Publications},
keywords = {topological algebra; -algebra; Mackey -algebra; locally pseudoconvex algebra; locally convex algebra; locally bounded algebra; von Neumann bornology; pseudoconvex bornology; spectrum; spectral radius; radius of boundedness},
language = {eng},
number = {1},
pages = {21-33},
title = {Topological algebras with pseudoconvexly bounded elements},
url = {http://eudml.org/doc/281651},
volume = {67},
year = {2005},
}

TY - JOUR
AU - Mati Abel
TI - Topological algebras with pseudoconvexly bounded elements
JO - Banach Center Publications
PY - 2005
VL - 67
IS - 1
SP - 21
EP - 33
AB - It is shown that every commutative sequentially bornologically complete Hausdorff algebra A with bounded elements is representable in the form of an (algebraic) inductive limit of an inductive system of locally bounded Fréchet algebras with continuous monomorphisms if the von Neumann bornology of A is pseudoconvex. Several classes of topological algebras A for which $r_A(a) ≤ β_A(a)$ or $r_A(a) = β_A(a)$ for each a ∈ A are described.
LA - eng
KW - topological algebra; -algebra; Mackey -algebra; locally pseudoconvex algebra; locally convex algebra; locally bounded algebra; von Neumann bornology; pseudoconvex bornology; spectrum; spectral radius; radius of boundedness
UR - http://eudml.org/doc/281651
ER -

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