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Generators for algebras dense in L p -spaces

Alexander J. Izzo, Bo Li (2013)

Studia Mathematica

For various L p -spaces (1 ≤ p < ∞) we investigate the minimum number of complex-valued functions needed to generate an algebra dense in the space. The results depend crucially on the regularity imposed on the generators. For μ a positive regular Borel measure on a compact metric space there always exists a single bounded measurable function that generates an algebra dense in L p ( μ ) . For M a Riemannian manifold-with-boundary of finite volume there always exists a single continuous function that generates...

Generators of maximal left ideals in Banach algebras

H. G. Dales, W. Żelazko (2012)

Studia Mathematica

In 1971, Grauert and Remmert proved that a commutative, complex, Noetherian Banach algebra is necessarily finite-dimensional. More precisely, they proved that a commutative, complex Banach algebra has finite dimension over ℂ whenever all the closed ideals in the algebra are (algebraically) finitely generated. In 1974, Sinclair and Tullo obtained a non-commutative version of this result. In 1978, Ferreira and Tomassini improved the result of Grauert and Remmert by showing that the statement...

Genèse des premiers espaces vectoriels de fonctions

Jean-Luc Dorier (1996)

Revue d'histoire des mathématiques

Cet article examine comment la notion d’espace vectoriel de fonctions s’est peu à peu imposée dans l’analyse entre 1880 et 1930 environ. Malgré certaines approches formelles précoces, les questions linéaires en dimension infinie sont longtemps restées marquées par l’analogie avec la dimension finie, que l’on traitait alors à l’aide des déterminants. Nous regardons comment l’étude de l’équation de Fredholm d’une part, en particulier le travail de Hilbert, et l’émergence de notions topologiques d’autre...

Geometría de gramianos en el espacio de Hilbert.

Pedro J. Burillo López, Joaquín Aguilella Almer (1981)

Stochastica

The purpose of the Part I of this paper is to develop the geometry of Gram's determinants in Hilbert space. In Parts II and III a generalization is given of the Pythagorean theorem and triangular inequality for finite vector families.

Geometric characterization of L₁-spaces

Normuxammad Yadgorov, Mukhtar Ibragimov, Karimbergen Kudaybergenov (2013)

Studia Mathematica

The paper is devoted to a description of all real strongly facially symmetric spaces which are isometrically isomorphic to L₁-spaces. We prove that if Z is a real neutral strongly facially symmetric space such that every maximal geometric tripotent from the dual space of Z is unitary, then the space Z is isometrically isomorphic to the space L₁(Ω,Σ,μ), where (Ω,Σ,μ) is an appropriate measure space having the direct sum property.

Geometric, spectral and asymptotic properties of averaged products of projections in Banach spaces

Catalin Badea, Yuri I. Lyubich (2010)

Studia Mathematica

According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex combinations of products of some projections in a complex Banach space. The latter is assumed uniformly convex or uniformly smooth for the orthoprojections, or reflexive for more special projections, in particular, for the hermitian ones. In all cases the proof...

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