You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Two-Norm Spaces and Decompositions of Banach Spaces. II
P. K. Subramanian and S. Rothman
Transactions of the American Mathematical Society
Vol. 181 (Jul., 1973), pp. 313-327
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1996635
Page Count: 15
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
Let X be a Banach space, Y a closed subspace of X*. One says X is Y-reflexive if the canonical imbedding of X onto Y* is an isometry and Y-pseudo reflexive if it is a linear isomorphism onto. If X has a basis and Y is the closed linear span of the corresponding biorthogonal functionals, necessary and sufficient conditions for X to be Y-pseudo reflexive are due to I. Singer. To every B-space X with a decomposition we associate a canonical two-norm space Xs and show that the properties of Xs, in particular its γ-completion, may be exploited to give different proofs of Singer's results and, in particular, to extend them to B-spaces with decompositions. This technique is then applied to a study of direct sum of B-spaces with respect to a BK space. Necessary and sufficient conditions for such a space to be reflexive are obtained.
Transactions of the American Mathematical Society © 1973 American Mathematical Society