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Metric generalizations of Banach algebras

W. Żelazko — 1965

CONTENTSPRELIMINARIES§ 0. Introduction.......................................................................................................................................................................3§ 1. Definitions and notation.................................................................................................................................................5Chapter ILOCALLY BOUNDED ALGEBRAS§ 2. Basic facts and examples..............................................................................................................................................6§...

Functional continuity of commutative m-convex $B_{0}$ -algebras with countable maximal ideal spaces

W. Żelazko — 1987

Colloquium Mathematicae

On m-convex $B_{0}$ -algebras of type ES

W. Żelazko — 1969

Colloquium Mathematicae

On multiplicative linear functionals

W. Żelazko — 1973

Colloquium Mathematicae

A non-locally convex topological algebra with all commutative subalgebras locally convex

W. Żelazko — 1996

Studia Mathematica

We construct a complete multiplicatively pseudoconvex algebra with the property announced in the title. This solves Problem 25 of [6].

On topologization of countably generated algebras

W. Żelazko — 1994

Studia Mathematica

We prove that any real or complex countably generated algebra has a complete locally convex topology making it a topological algebra. Assuming the continuum hypothesis, it is the best possible result expressed in terms of the cardinality of a set of generators. This result is a corollary to a theorem stating that a free algebra provided with the maximal locally convex topology is a topological algebra if and only if the number of variables is at most countable. As a byproduct we obtain an example...

A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.

W. Żelazko — 1996

Studia Mathematica

We construct two examples of complete multiplicatively convex algebras with the property that all their maximal commutative subalgebras and consequently all commutative closed subalgebras are Banach algebras. One of them is non-metrizable and the other is metrizable and non-Banach. This solves Problems 12-16 and 22-24 of [7].

Concerning entire functions in $B_{0}$ -algebras

W. Żelazko — 1994

Studia Mathematica

We construct a non-m-convex non-commutative $B_{0}$ -algebra on which all entire functions operate. Our example is also a Q-algebra and a radical algebra. It follows that some results true in the commutative case fail in general.

Some remarks on topological algebras

W. Żelazko — 1963

Studia Mathematica

A semitopological algebra without proper closed subalgebras

W. Żelazko — 1998

Colloquium Mathematicae

To Czesław Ryll-Nardzewski on his 70th birthday

Generation of B(X) two commutative subalgebras - results and open problems

W. Żelazko — 1994

Banach Center Publications

The strongest vector space topology is locally convex on separable linear subspaces

W. Żelazko — 1997

Annales Polonici Mathematici

Let X be a real or complex vector space equipped with the strongest vector space topology $τ_{m a x}$ . Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.

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Currently displaying 1 – 20 of 56

Metric generalizations of Banach algebras

Functional continuity of commutative m-convex $B_{0}$ -algebras with countable maximal ideal spaces

On m-convex $B_{0}$ -algebras of type ES

On multiplicative linear functionals

A non-locally convex topological algebra with all commutative subalgebras locally convex

On topologization of countably generated algebras

A non-Banach in-convex algebra all of whose closed commutative subalgebras are Banach algebras.

Concerning entire functions in $B_{0}$ -algebras

Some remarks on topological algebras

A semitopological algebra without proper closed subalgebras

Generation of B(X) two commutative subalgebras - results and open problems

The strongest vector space topology is locally convex on separable linear subspaces

Concerning topologization of real or complex algebras

On strongly closed subalgebras of B(X)

A subfield of a complex Banach algebra is not necessarily topologically isomorphic to a subfield of ℂ

On topological divisors of zero in p-normed algebras without unit

An axiomatic approach to joint spectra I

On certain class of non-removable ideals in Banach algebras

On maximal ideals in commutative m-convex algebras

On a problem concerning joint approximate point spectra