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 |
Acceso al artículo completo |