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Totally Incomparable Banach Spaces and Three‐Space Banach Space Ideals
Author(s) -
Alvarez Teresa,
Gonzalez Manuel,
Onieva Victor M.
Publication year - 1987
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19871310108
Subject(s) - mathematics , banach space , norm (philosophy) , linear subspace , space (punctuation) , dual norm , pure mathematics , lp space , banach manifold , assertion , discrete mathematics , computer science , political science , law , programming language , operating system
In this paper we present four methods to generate three‐space B ANACH space ideals. They are based on the concept of total incomparability of H. P. R OSENTHAL and on a dual concept, total coincomparability, which is here introduced. We use the assertion that the sum of two totally incomparable closed subspaces of a B ANACH space is norm‐closed, which is shown by means of an easier and more natural proof than that of R OSENTHAL [10], and an analogous property about the total coincomparability. Several well‐known ideals are obtained with the above methods, and so they are three‐space ideals.