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Displaying 381 – 400 of 409

Topological algebras with pseudoconvexly bounded elements

Mati Abel (2005)

Banach Center Publications

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 $r_{A} (a) \leq β_{A} (a)$ or $r_{A} (a) = β_{A} (a)$ for each a ∈ A are described.

Topological localization in Fréchet algebras.

Batildo Requejo (1994)

Extracta Mathematicae

Topologically Invertible Elements and Topological Spectrum

Mati Abel, Wiesław Żelazko (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Properties of topologically invertible elements and the topological spectrum of elements in unital semitopological algebras are studied. It is shown that the inversion $x \mapsto x^{- 1}$ is continuous in every invertive Fréchet algebra, and singly generated unital semitopological algebras have continuous characters if and only if the topological spectrum of the generator is non-empty. Several open problems are presented.

Totally convex algebras

Dieter Pumplün, Helmut Röhrl (1992)

Commentationes Mathematicae Universitatis Carolinae

By definition a totally convex algebra $A$ is a totally convex space $| A |$ equipped with an associative multiplication, i.eȧ morphism $μ : | A | \otimes | A | ⟶ | A |$ of totally convex spaces. In this paper we introduce, for such algebras, the notions of ideal, tensor product, unitization, inverses, weak inverses, quasi-inverses, weak quasi-inverses and the spectrum of an element and investigate them in detail. This leads to a considerable generalization of the corresponding notions and results in the theory of Banach spaces.

Trace and determinant in Banach algebras

Bernard Aupetit, H. Mouton (1996)

Studia Mathematica

We show that the trace and the determinant on a semisimple Banach algebra can be defined in a purely spectral and analytic way and then we obtain many consequences from these new definitions.

Über die Ecken des numerischen Wertebereches in einer Banachalgebra.

Bernd Schmidt (1972)

Mathematische Zeitschrift

Über die Ecken des numerischen Wertebereiches in einer Banachalgebra. II.

Bernd Schmidt (1972)

Mathematische Zeitschrift

Ultraproducts in Banach space theory.

Stefan Heinrich (1980)

Journal für die reine und angewandte Mathematik

Uniformly continuous functionals on Banach algebras

Anthony To-Ming Lau (1987)

Colloquium Mathematicae

Unitary Banach algebras

Julio Becerra Guerrero, Simon Cowell, Ángel Rodríguez Palacios, Geoffrey V. Wood (2004)

Studia Mathematica

In a Banach algebra an invertible element which has norm one and whose inverse has norm one is called unitary. The algebra is unitary if the closed convex hull of the unitary elements is the closed unit ball. The main examples are the C*-algebras and the ℓ₁ group algebra of a group. In this paper, different characterizations of unitary algebras are obtained in terms of numerical ranges, dentability and holomorphy. In the process some new characterizations of C*-algebras are given.

Unité Et Semi-Normes Dans Les Algèbres Localement Convexes.

Mohamed Oudadess (1982)

Revista colombiana de matematicas

Universal estimates of the spectral radius

Vlastimil Pták (1982)

Banach Center Publications

Vector-valued invariant means on spaces of bounded linear maps

Mahshid Dashti, Rasoul Nasr-Isfahani, Sima Soltani Renani (2013)

Colloquium Mathematicae

Let 𝓐 be a Banach algebra and let ℳ be a W*-algebra. For a homomorphism Φ from 𝓐 into ℳ, we introduce and study ℳ -valued invariant Φ-means on the space of bounded linear maps from 𝓐 into ℳ. We establish several characterizations of existence of an ℳ -valued invariant Φ-mean on B(𝓐,ℳ). We also study the relation between existence of an ℳ -valued invariant Φ-mean on B(𝓐,ℳ) and amenability of 𝓐. Finally, for a character ϕ of 𝓐, we give some descriptions for ϕ-amenability of 𝓐 in terms of ℳ...

Weak approximate identities and multipliers

David Johnson, Charles Lahr (1982)

Studia Mathematica

Weak invertibility and strong spectrum

Michael Meyer (1993)

Studia Mathematica

A notion of weak invertibility in a unital associative algebra A and a corresponding notion of strong spectrum of an element of A is defined. It is shown that many relationships between the Jacobson radical, the group of invertibles and the spectrum have analogues relating the strong radical, the set of weakly invertible elements and the strong spectrum. The nonunital case is also discussed. A characterization is given of all (submultiplicative) norms on A in which every modular maximal ideal M...

When a unital F-algebra has all maximal left (right) ideals closed?

W. Żelazko (2006)

Studia Mathematica

We prove that a real or complex unital F-algebra has all maximal left ideals closed if and only if the set of all its invertible elements is open. Consequently, such an algebra also automatically has all maximal right ideals closed.

When unit groups of continuous inverse algebras are regular Lie groups

Helge Glöckner, Karl-Hermann Neeb (2012)

Studia Mathematica

It is a basic fact in infinite-dimensional Lie theory that the unit group $A^{\times}$ of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group $A^{\times}$ is regular in Milnor’s sense. Notably, $A^{\times}$ is regular if A is Mackey-complete and locally m-convex.

Where to find the image of a derivation

Martin Mathieu (1994)

Banach Center Publications

With this paper, we intend to provide an overview of some recent work on a problem on unbounded derivations of Banach algebras that still defies solution, the non-commutative Singer-Wermer conjecture. In particular, we discuss several global as well as local properties of derivations entailing quasinilpotency in the image.

Zur Spektralinvarianz von Algebren von Pseudodifferentialoperatoren in der Lp-Theorie.

Johannes Ueberberg (1988)

Manuscripta mathematica

$ϕ$ -multipliers on a class of topological algebras

Ali Naziri-Kordkandi (2022)

Mathematica Bohemica

In this paper, we generalize the concept of $ϕ$ -multipliers on Banach algebras to a class of topological algebras. Then the characterizations of $ϕ$ -multipliers are investigated in these algebras.

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