Projections on tensor products of Banach spaces

Abstract

We characterize norm hermitian operators on classes of tensor products of Banach spaces and derive results for the particular settings of injective and projective tensor products. We provide a characterization of bi-circular and generalized bi-circular projections on tensor products of Banach spaces supporting only dyadic surjective isometries. Mathematics Subject Classification (2000). Primary 30D55; Secondary 30D05.Keywords. Isometry, bi-circular projections, generalized bi-circular projections, injective and projective tensor products of Banach spaces. Introduction.In this paper, we characterize the structure of norm hermitian operators on tensor products of Banach spaces in which the only surjective isometries are of dyadic type. Khalil in [9], Khalil-Salem in [8], and Jarosz in [11] provided classifications of surjective isometries for different tensor products of Banach spaces that assure the existence of spaces with such isometries. The structure of norm hermitian operators allows an easy characterization of those operators that are also hermitian projections. Such characterization can be transcribed for bicircular projections, as established by Jamison in [10]. The last section extends previous results to the more general case of generalized bi-circular projections, introduced in [7], and provides characterizations of these projections in a variety of tensor product spaces. Characterizations of generalized bi-circular projections in various Banach spaces can be found in [3], [4] and [13].