Factorization through Hilbert space and the dilation of L(X,Y)-valued measures
Volume 107 / 1993
Studia Mathematica 107 (1993), 101-113
DOI: 10.4064/sm-107-2-101-113
Abstract
We present a general necessary and sufficient algebraic condition for the spectral dilation of a finitely additive L(X,Y)-valued measure of finite semivariation when X and Y are Banach spaces. Using our condition we derive the main results of Rosenberg, Makagon and Salehi, and Miamee without the assumption that X and/or Y are Hilbert spaces. In addition we relate the dilation problem to the problem of factoring a family of operators through a single Hilbert space.
