# Topological algebras with pseudoconvexly bounded elements

Banach Center Publications (2005)

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

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topMati 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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