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A note on operator Banach spaces containing a complemented copy of c0 (2000)

Paneque, F. ; Piñeiro, C.

Springer

Archiv der Mathematik 75 (2000), S. 370-375

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ISSN: 1420-8938

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract. Let X and Y Banach spaces. Two new properties of operator Banach spaces are introduced. We call these properties “boundedly closed” and “d-boundedly closed”. Among other results, we prove the following one. Let ${\cal U}(X, Y)$ an operator Banach space containing a complemented copy of c 0. Then we have: 1) If ${\cal U}(X, Y)$ is boundedly closed then Y contains a copy of c 0. 2) If ${\cal U}(X, Y)$ is d-boundedly closed, then X * or Y contains a copy of c 0.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s000130050517

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