Relatively open operators and the ubiquitous concept.

Título inglés Relatively open operators and the ubiquitous concept.
Título español Operadores relativamente abiertos y concepto de ubicuidad.
Autor/es Cross, R. W.
Organización Dep. Math. Univ. Cape Town, Rondebosch, Africa del Sur
Revista 0214-1493
Publicación 1994, 38 (1): 69-79, 23 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés A linear operator T: D(T) Ì X → Y, when X and Y are normed spaces, is called ubiquitously open (UO) if every infinite dimensional subspace M of D(T) contains another such subspace N for which T|N is open (in the relative sense). The following properties are shown to be equivalent: (i) T is UO, (ii) T is ubiquitously almost open, (iii) no infinite dimensional restriction of T is injective and precompact, (iv) either T is upper semi-Fredholm or T has finite dimensional range, (v) for each infinite dimensional subspace M of D(T), we have dim(T|M)-1(0) + Δ(T|M) > 0. In case T is closed and X and Y are Banach spaces, T is UO if and only if TM Ì TM for every linear subspace M of X.
Clasificación UNESCO 120201
Palabras clave español Operadores lineales ; Espacios normados ; Bola unidad
Código MathReviews MR1291954
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