Polynomials in operator space theory

Multivariate Orthogonal Polynomials and Operator Theory

The multivariate orthogonal polynomials are related to a family of commuting selfadjoint operators. The spectral theorem for these operators is used to prove that a polynomial sequence satisfying a vector-matrix form of the three-term relation is orthonormal with a determinate measure.

Methods of Kreĭn Space Operator Theory

The author was originally led to Krĕın space operator theory by a problem of L. de Branges concerning the coefficients of univalent functions. The particular question was resolved in the negative, but the operator methods used to show this are related to other areas which remain currently active, such as the study of generalized Schur and Nevanlinna functions. The methods are of a general natur...

OPERATOR SPACE Lp EMBEDDING THEORY I

Let X 1 and X 2 be subspaces of quotients of R ⊕ OH and C ⊕ OH respectively. We use new free probability techniques to construct a completely isomorphic embedding of the Haagerup tensor product X 1 ⊗ h X 2 into the predual of a sufficiently large QWEP von Neumann algebra. As an immediate application, given any 1 < q ≤ 2, our result produces a completely isomorphic embedding of ℓq (equipped with...

OPERATOR THEORY ON HILBERT SPACE Class notes

Spectral Theory of Operator Measures in Hilbert Space

In §2 the spaces L2(Σ,H) are described; this is a solution of a problem posed by M. G. Krĕın. In §3 unitary dilations are used to illustrate the techniques of operator measures. In particular, a simple proof of the Năımark dilation theorem is presented, together with an explicit construction of a resolution of the identity. In §4, the multiplicity function NΣ is introduced for an arbitrary (non...