In this paper we study the operator inequality φ(X) ≤ X and the operator equation φ(X) = X, where φ is a w∗-continuous positive (resp. completely positive) linear map on B(H). We show that their solutions are in one-to-one correspondence with a class of Poisson transforms on Cuntz-Toeplitz C∗-algebras, if φ is completely positive. Canonical decompositions, ergodic type theorems, and lifting the...

In this note we show that an unbounded regular operator t on Hilbert C∗modules over an arbitrary C∗ algebra A has polar decomposition if and only if the closures of the ranges of t and |t| are orthogonally complemented, if and only if the operators t and t∗ have unbounded regular generalized inverses. For a given C∗-algebra A any densely defined A-linear closed operator t between Hilbert C∗-mod...

In this article we initiate a systematic study of irreducible weight modules over direct limits of reductive Lie algebras, and in particular over the simple Lie algebras A(∞), B(∞), C(∞) and D(∞). Our main tool is the shadow method introduced recently in [DMP]. The integrable irreducible modules are an important particular class and we give an explicit parametrization of the finite integrable m...

The purpose of this paper is to investigate the homotopy theory of C*algebras of the formC0(X)⊗K, whereX is a finite connected CWcomplex with base point; hereC0(X) is theC*-algebra of continuous complex-valued functions which vanish at the base point, K is the C*-algebra of compact operators on a separable infinite dimensional complex Hilbert space, and a homotopy between two C*-algebra maps is...

By computing the completely bounded norm of flip map on Haagerup tensor product [Formula: see text] associated to a pair continuous mappings locally compact Hausdorff spaces text], we establish simple characterization Beck-Chevalley condition for base change operator modules over commutative text]-algebras, and descent theorem fields Hilbert spaces.

Let C denote the category of Hilbert modules which are similar to contractive Hilbert modules. It is proved that if H0, H ∈ C and if H1 is similar to an isometric Hilbert module, then the sequence 0 → H0 → H → H1 → 0 splits. Thus the isometric Hilbert modules are projective in C. It follows that ExtC (K, H) = 0, whenever n > 1, for H, K ∈ C. In addition, it is proved that (Hilbert modules simil...