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A characterization of M-Summands

Published online by Cambridge University Press:  24 October 2008

Richard Evans
Richard Evans
Affiliation:
Freie Universität, Berlin
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Extract

In the structure theory of Banach spaces as developed in (1), an important role is played by subspaces which are the ranges of projections having norm properties akin to those of the classical Banach spaces. A linear projection e on a Banach space V is called an M-projection if

and an L-projection if, instead

A closed subspace J of V is called an M-Summand if it is the range of an M-projection and an M-Ideal if J0 is the range of an L-projection in V′. Every M-Summand is an M-Ideal but the reverse is false.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 76 , Issue 1 , July 1974 , pp. 157 - 159
Copyright
Copyright © Cambridge Philosophical Society 1974

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References

REFERENCES

(1)Alfsen, E. M. and Effros, E.Structure in real Banach spaces. Parts I and II. Ann. of Math. 96 (1972), 98–173.CrossRefGoogle Scholar