We consider a Hilbert space of entire analytic functions on non-separable space, associated with Fock space. show that under some conditions operators, like the differentiation operators and translation are topologically transitive in this

Let X be a compact Hausdorff space and let H be a separable Hilbert space. We prove that the group of all order automorphisms of the C∗-algebra C(X)⊗ B(H) is algebraically reflexive.

We show that the Hilbert space is coarsely embeddable into any lp for 1 ≤ p < ∞. In particular, this yields new characterizations of embeddability of separable metric spaces into the Hilbert space. Coarse embeddings were defined by M. Gromov [Gr] to express the idea of inclusion in the large scale geometry of groups. G. Yu showed later that the case when a finitely generated group with a word l...

We prove that if a non-atomic separable Banach lattice in a weak Hilbert space, then it is lattice isomorphic to L2(0, 1). Introduction This note is to be considered as an addendum to [3], where an extensive study of Banach lattices, which are weak Hilbert spaces, was made. We prove that if a non-atomic separable Banach lattice is a weak Hilbert space then it is lattice isomorphic to L2(0, 1). ...

Let H be a separable, infinite dimensional complex Hilbert space and let B(H) be the algebra of bounded linear operators on H. An operator T∈ B(H) is said to be normal if T ∗T = TT ∗, subnormal if T is the restriction of a normal operator (acting on a Hilbert space K ⊇ H) to an invariant subspace, and hyponormal if T ∗T ≥ TT ∗. The Bram-Halmos criterion for subnormality states that an operator ...

Using Paschke-Higson Duality [Hig][Pa], we get a natural index pairingKi(A)×Ki+1(DΦ) → Z where i = 0, 1(mod2) and A is a separable C ∗ -algebra, Φ is a representation of A on a separable Hilbert space H. We prove this is a special case of Kasparov Product [Kas].

An analog of the Whittaker-Shannon-Kotel′nikov sampling theorem is derived for functions with values in a separable Hilbert space. The proof uses the concept of frames and frame operators in a Hilbert space. One of the consequences of this theorem is that it allows us to derive sampling theorems associated with boundary-value problems and some homogeneous integral equations, which in turn gives...

Schroedinger equation on a Hilbert space H, represents a linear Hamiltonian dynamical system on the space of quantum pure states, the projective Hilbert space PH. Separable states of a bipartite quantum system form a special submanifold of PH. We analyze the Hamiltonian dynamics that corresponds to the quantum system constrained on the manifold of separable states, using as an important example...

in a real separable Hilbert space H driven by an infinite dimensional cylindrical symmetric Lévy process Z = (Zt). The process Z may take values in a Hilbert space 1 Supported by the M.I.U.R. research projects Prin 2004 and 2006 “Kolmogorov equations” and by the Polish Ministry of Science and Education project 1PO 3A 034 29 “Stochastic evolution equations with Lévy noise”. 2 Supported by the Po...