# Relatively open operators and the ubiquitous concept.

Publicacions Matemàtiques (1994)

- Volume: 38, Issue: 1, page 69-79
- ISSN: 0214-1493

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topCross, R. W.. "Relatively open operators and the ubiquitous concept.." Publicacions Matemàtiques 38.1 (1994): 69-79. <http://eudml.org/doc/41204>.

@article{Cross1994,

abstract = {A linear operator T: D(T) ⊂ 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 ⊂ TM for every linear subspace M of X.},

author = {Cross, R. W.},

journal = {Publicacions Matemàtiques},

keywords = {Operadores lineales; Espacios normados; Bola unidad; relatively open operators; ubiquitously almost open; semi-Fredholm},

language = {eng},

number = {1},

pages = {69-79},

title = {Relatively open operators and the ubiquitous concept.},

url = {http://eudml.org/doc/41204},

volume = {38},

year = {1994},

}

TY - JOUR

AU - Cross, R. W.

TI - Relatively open operators and the ubiquitous concept.

JO - Publicacions Matemàtiques

PY - 1994

VL - 38

IS - 1

SP - 69

EP - 79

AB - A linear operator T: D(T) ⊂ 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 ⊂ TM for every linear subspace M of X.

LA - eng

KW - Operadores lineales; Espacios normados; Bola unidad; relatively open operators; ubiquitously almost open; semi-Fredholm

UR - http://eudml.org/doc/41204

ER -