Tirthankar Bhattacharyya
Completely bounded kernels.
Thu, 01/21/2010 - 16:01 — SomNambulAuthors: Tirthankar Bhattacharyya, Michael A. Dritschel, Christopher S. Todd
Subjects: Operator Algebras
AbstractIt is a classical result that scalar valued positive kernels have Kolmogorov
decompositions. This has been extended in various ways, culminating in a
version of the Kolmogorov decomposition for completely positive L(A,B) valued
kernels, A and B C*-algebras, due to Barreto, Bhat, Liebscher and Skeide.Coincidence of Schur Multipliers of the Drury-Arveson Space.
Thu, 11/19/2009 - 16:01 — SomNambulAuthors: Angshuman Bhattacharya, Tirthankar Bhattacharyya
Subjects: Functional Analysis
AbstractIn a purely multi-variable setting (i.e., the issues discussed in this note
are not interesting in the single variable operator theory setting), we show
that the coincidence of two operator valued Schur class multipliers of a
certain kind on the Drury-Arveson space is characterized by the fact that the
associated colligations (or a variant, obtained canonically) are `unitarily
coincident' in a sense to be made precise in the last section of this article.Complete Pick Positivity and Unitary Invariance.
Wed, 10/28/2009 - 16:01 — SomNambulAuthors: Angshuman Bhattacharya, Tirthankar Bhattacharyya
Subjects: Functional Analysis
AbstractThe characteristic function for a contraction is a classical complete unitary
invariant devised by Sz.-Nagy and Foias. Just as a contraction is related to
the Szego kernel $k_S(z,w) = (1 - z\ow)^{-1}$ for $|z|, |w| < 1$, by means of
$(1/k_S)(T,T^*) \ge 0$, we consider an arbitrary open connected domain $\Omega$
in $\BC^n$, a complete Nevanilinna-Pick kernel $k$ on $\Omega$ and a tuple $T =
(T_1, ..., T_n)$ of commuting bounded operators on a complex separable Hilbert
space $\clh$ such that $(1/k)(T,T^*) \ge 0$.
User login
