On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

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...

We study spectral asymptotics and resolvent bounds for non-selfadjoint perturbations of selfadjoint h-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part is completely integrable. Spectral contributions coming from rational invariant Lagrangian tori are analyzed. Estimating the tunnel effect between strongly irrational (Diophantine) and rational...

We define a new topology, weaker than the gap topology, on the space of selfadjoint unbounded operators on a separable Hilbert space. We show that the subspace of selfadjoint Fredholm operators represents the functor K from the category of compact spaces to the category of abelian groups and prove a similar result for K. We define the spectral flow of a continuous path of selfadjoint Fredholm o...

Perturbations AT of a selfadjoint operator A by symmetric finite rank operators T from H2(A) to H−2(A) are studied. The finite dimensional family of selfadjoint extensions determined by AT is given explicitly.

In this paper, we construct, for a certain class of semigroup dynamical systems, two operator algebras that are universal with respect to their corresponding covariance conditions: one being selfadjoint, and another nonselfadjoint. We prove the C*-envelope nonselfadjoint algebra is precisely selfadjoint one. This result leads number new examples C*-envelopes, many from fields commutative rings....

We describe the convex set of the eigenvalues of hermitian matrices which are majorized by sum of m hermitian matrices with prescribed eigenvalues. We extend our characterization to selfadjoint nonnegative (definite) compact operators on a separable Hilbert space. We give necessary and sufficient conditions on the eigenvalue sequence of a selfadjoint nonnegative compact operator of trace class ...

We study the selfadjoint time operator recently constructed by one of the authors. We will show that this time operator must be interpreted as a “selfadjoint variant” of the time operator.

Let H be a Hilbert space, L(H) the algebra of all bounded linear operators on H and 〈 , 〉A : H×H → C the bounded sesquilinear form induced by a selfadjoint A ∈ L(H), 〈ξ, η〉A = 〈Aξ, η〉, ξ, η ∈ H. Given T ∈ L(H), T is A-selfadjoint if AT = T ∗A. If S ⊆ H is a closed subspace, we study the set of A-selfadjoint projections onto S, P(A,S) = {Q ∈ L(H) : Q = Q , R(Q) = S , AQ = Q∗A} for different choi...