A REPRESENTATION THEOREM FOR NORMS IN HILBERT SPACE

A Representation Theorem for Schauder Bases in Hilbert Space

A sequence of vectors {f1, f2, f3, . . . } in a separable Hilbert space H is said to be a Schauder basis for H if every element f ∈ H has a unique norm-convergent expansion f = ∑ cnfn. If, in addition, there exist positive constants A and B such that A ∑ |cn| ≤ ∥∥∥∑ cnfn∥∥∥2 ≤ B∑ |cn|, then we call {f1, f2, f3, . . . } a Riesz basis. In the first half of this paper, we show that every Schauder ...

A Splitting Theorem for Isoparametric Submanifolds in Hilbert Space

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

A Morita Theorem for Algebras of Operators on Hilbert Space

We show that two operator algebras are strongly Morita equivalent (in the sense of Blecher, Muhly and Paulsen) if and only if their categories of operator modules are equivalent via completely contractive functors. Moreover, any such functor is completely isometrically isomorphic to the Haagerup tensor product (= interior tensor product) with a strong Morita equivalence bimodule. Date: Septembe...

A Carathéodory theorem for the bidisk via Hilbert space methods

If φ is an analytic function bounded by 1 on the bidisk D2 and τ ∈ ∂(D2) is a point at which φ has an angular gradient ∇φ(τ) then ∇φ(λ) → ∇φ(τ) as λ → τ nontangentially in D2. This is an analog for the bidisk of a classical theorem of Carathéodory for the disk. For φ as above, if τ ∈ ∂(D2) is such that the lim inf of (1− |φ(λ)|)/(1− ‖λ‖) as λ → τ is finite then the directional derivative D−δφ(τ...