Operator Matrices as Generators of Cosine Operator Functions

Computation of Functions of Certain Operator Matrices

This note gives a simple method to compute the entries of holomorphic functions of a 2× 2 block or operator matrix which can be written as a product. To illustrate this method, the entries are given for the exponential, fractional powers and inverse of such operator matrices. If H and K are Hilbert spaces, we denote the space of bounded linear operators from H to K by L(H,K). Our main result is...

Further inequalities for operator space numerical radius on 2*2 operator ‎matrices

‎We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$‎, ‎when $X$ is a numerical radius operator space‎. ‎These inequalities contain some upper and lower bounds for operator space numerical radius.

Operator Interpretation of Resonances Generated by Some Operator Matrices

We consider the analytic continuation of the transfer function for a 2 × 2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the transfer-function spectrum including resonances situated on the unphysical sheets neighboring the physical sheet. On this basis, completeness and basis prope...

Stability for generators of cosine functions

Properties of multivalent functions associated with certain integral operator

Let A(p) denote the class of functions which are analytic in the open unit disk U. By making use of certain integral operator,we obtain some interesting properties of multivalent analytic functions.