M-structure in Banach spaces
- 1 July 1967
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 63 (3) , 613-629
- https://doi.org/10.1017/s0305004100041591
Abstract
L-structure in a Banach space X was defined in (3) by L-projections, that is projections P satisfyingfor all x ∈ X. The significance of L-structure is shown by the following facts: (1) All L-projections on X commute and together form a complete Boolean algebra. (2) X can be isometrically represented as a vector-valued L1 on a measure space constructed from the Boolean algebra of its L-projections (2). (3) L1-spaces in the ordinary sense are characterized among Banach spaces by properties equivalent to having so many L-projections that the representation in (2) is everywhere one-dimensional.Keywords
This publication has 4 references indexed in Scilit:
- Extension of compact operatorsMemoirs of the American Mathematical Society, 1964
- L-Structure in L-SpacesTransactions of the American Mathematical Society, 1960
- Concrete Representation of Abstract (M)-Spaces (A characterization of the Space of Continuous Functions)Annals of Mathematics, 1941
- Concrete Representation of (M)-SpacesAnnals of Mathematics, 1941