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INICIO | 14 de abril de 2024
  

Isomorphically isometric probabilistic normed linear spaces.

Título inglés Isomorphically isometric probabilistic normed linear spaces.
Título español Espacios lineales normados probabilísticos isomórficamente isométricos.
Autor/es Sherwood, Howard
Organización Dep. Math. Stat. Univ. Central Florida, Orlando (Florida), Estados Unidos
Revista 0210-7821
Publicación 1979, 3 (2): 71-77, 3 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés Probabilistic normed linear spaces (briefly PNL spaces) were first studied by A. N. Serstnev in [1]. His definition was motivated by the definition of probabilistic metric spaces (PM spaces) which were introduced by K. Menger and subsequebtly developed by A. Wald, B. Schweizer, A. Sklar and others.
In a previuos paper [2] we studied the relationship between two important classes of PM spaces, namely E-spaces and pseudo-metrically generated PM spaces. We showed that a PM space is pseudo-metrically generated if and only if it is isometric to an E-space. In this paper we extend these ideas and results to PNL spaces. We define E-norm spaces and pseudo-norm-generated PNL spaces and show that a PNL space is pseudo-norm-generated if and only if it is isomorphically isometric to an E-norm space. In order to preserve the algebraic structure in a meaningful way we require new constructions which differ considerably from those given in the original PM space setting.
Clasificación UNESCO 120225 ; 120804
Palabras clave español Espacios normados ; Espacios probabilísticos ; Espacios métricos ; Isometría
Código MathReviews MR0556648
Código Z-Math Zbl 0432.60014
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
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