The classical identification of the predual of B(H) (the algebra of all bounded operators on a Hilbert space H) with the projective operator space tensor product H⊗̂H is extended to the context of Hilbert modules over commutative von Neumann algebras. Each bounded module homomorphism b between Hilbert modules over a general C∗-algebra is shown to be completely bounded with ‖b‖cb = ‖b‖. The so ca...

We regard the Schrr odinger{Poisson system arising from the modelling of an electron gas with reduced dimension in a bounded up to three{ dimensional domain and establish the method of steepest descent. The electro-static potentials of the iteration scheme will converge uniformly on the spatial domain. To get this result we investigate the Schrr odinger operator, the Fermi level and the quantum...

Let D be a bounded symmetric domain in C and let ψ be a complex-valued holomorphic function on D. In this work, we determine the operator norm of the bounded multiplication operator with symbol ψ from the space of bounded holomorphic functions on D to the Bloch space of D when ψ fixes the origin. If no restriction is imposed on the symbol ψ, we have a formula for the operator norm when D is the...

Let E, F be exact operator spaces (for example subspaces of the C *-algebra K(H) of all the compact operators on an infinite dimensional Hilbert space H). We study a class of bounded linear maps u: E → F * which we call tracially bounded. In particular, we prove that every completely bounded (in short c.b.) map u: E → F * factors boundedly through a Hilbert space. This is used to show that the ...

The main result of the paper is the theorem giving a sufficient condition for the existence of a bounded analytic projection onto a holomorphic family of (generally infinite-dimensional) subspaces (a holomorphic sub-bundle of a trivial bundle). This sufficient condition is also necessary in the case of finite dimension or codimension of the bundle. A simple lemma of N. Nikolski connects the exi...

An algebra of bounded linear operators on a Hilbert space is called strongly compact whenever each of its bounded subsets is relatively compact in the strong operator topology. The concept is most commonly studied for two algebras associated with a single operator T : the algebra alg(T ) generated by the operator, and the operator’s commutant com(T ). This paper focuses on the strong compactnes...

The classical time-invariant Hankel-norm approximation problem is generalized to the time-varying context. The input-output operator of a time-varying bounded causal linear system acting in discrete time may be specified as a bounded upper-triangular operator T with block matrix entries Tij. For such an operator T, we will define the Hankel norm as a generalization of the time-invariant Hankel ...

We show that the symbol of a bounded composition operator on Wiener algebra Dirichlet series does not need to belong this algebra. Our example even gives an absolutely summing (hence compact) operator.

A completely bounded bilinear operator φ: M×M → M on a von Neumann algebra M is said to have a factorization in M if there exist completely bounded linear operators ψj , θj : M → M such that

Let R 2 be a bounded domain with Lipschitz boundary and let : ! R be a function which is measurable and bounded away from zero and innnity. We consider the divergence form elliptic operator