On the Cosine-Sine Operator Functional Equations
On the Cosine-Sine Operator Functional Equations (Short Communication)
On the cyclic elements of the shift operator in a weighted anisotropic space of holomorphic function in the polydisc.
On the (C,α) Cesàro bounded operators
For a given linear operator T in a complex Banach space X and α ∈ ℂ with ℜ (α) > 0, we define the nth Cesàro mean of order α of the powers of T by . For α = 1, we find , the usual Cesàro mean. We give necessary and sufficient conditions for a (C,α) bounded operator to be (C,α) strongly (weakly) ergodic.
On the (C,α) uniform ergodic theorem
We improve a recent result of T. Yoshimoto about the uniform ergodic theorem with Cesàro means of order α. We give a necessary and sufficient condition for the (C,α) uniform ergodicity with α > 0.
On the Davis-Kahan-Weinberger Solution of the Norm-Preserving Dilation Problem.
On the defect spectrum of an extension of a Banach space operator
Let be an operator acting on a Banach space . We show that between extensions of to some Banach space which do not increase the defect spectrum (or the spectrum) it is possible to find an extension with the minimal possible defect spectrum.
On the dependence of the orthogonal projector on deformations of the scalar product
We consider scalar products on a given Hilbert space parametrized by bounded positive and invertible operators defined on this space, and orthogonal projectors onto a fixed closed subspace of the initial Hilbert space corresponding to these scalar products. We show that the projector is an analytic function of the scalar product, we give the explicit formula for its Taylor expansion, and we prove some algebraic formulas for projectors.
On the differences of the consecutive powers of Banach algebra elements
Let A denote a complex unital Banach algebra. We characterize properties such as boundedness, relative compactness, and convergence of the sequence for an arbitrary x ∈ A, using σ(x) and resolvent conditions. Under these circumstances, we investigate elements in the peripheral spectrum, and give further conclusions, also involving the behaviour of and .
On the differentiability of functions of an operator
On the differentiability of mappings and convex functionals
On the differentiability of mappings in Banach spaces
On the Dirichlet Problem for Functions on the Extreme Boundary of a Compact Convex Set.
On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators.
On the eigenvalues of a class of hypo-elliptic operators. IV
Let be a selfadjoint classical pseudo-differential operator of order with non-negative principal symbol on a compact manifold. We assume that is hypoelliptic with loss of one derivative and semibounded from below. Then exp, , is constructed as a non-classical Fourier integral operator and the main contribution to the asymptotic distribution of eigenvalues of is computed. This paper is a continuation of a series of joint works with A. Menikoff.
On the eigenvalues which express antieigenvalues.
On the equations X=KXS and AX=XK
On the ergodic limits for unitary periodic propagators.
On the ergodic power function for invertible positive operators
On the ergodic theory of contractions