Ranges of bimodule projections and conditional expectations

Abstract

I would like to thank Prof. Richard M. Timoney for the care he took in supervising my PhD thesis.

Type-zero ternary corners

“…so that the kernel K can be regarded as a bimodule over the left and right C*-algebras of S (see [8,12]). Now we define the ternary corners in TROs which are our main object of investigation.…”

“…It is not difficult to prove that a sub-TRO S of the TRO T is a ternary corner if and only if there is a TRO-conditional expectation E on T such that E(T ) = S. See, e.g., [12,Theorem 4.1.3]. For a sub-TRO S ⊆ T we define…”

“…Let us look at an example (cf. also [12,Section 4.5]). Let H be an arbitrary non-zero complex Hilbert space.…”

“…TROs and their associated linking algebras share many common properties wherefore the application of operator algebraic methods simplifies the study of TROs that are not algebras themselves. Basic properties of TROs are discussed in, e.g., [1,8,10,12,15] and references therein.…”

“…The main tool that we use in the proofs are the contractive projections (equivalently, TRO-conditional expectations) on TROs and their properties. Projections and contractive projections on TROs are studied in [2,8,12,13,14], for example. Our results extend some results from [7] to the setting of TROs.…”