Powers and commutativity of selfadjoint operators.
Powers and Logarithms
There are applied power mappings in algebras with logarithms induced by a given linear operator D in order to study particular properties of powers of logarithms. Main results of this paper will be concerned with the case when an algebra under consideration is commutative and has a unit and the operator D satisfies the Leibniz condition, i.e. D(xy) = xDy + yDx for x, y ∈ dom D. Note that in the Number Theory there are well-known several formulae expressed by means of some combinations of powers...
Powers of class operators.
Powers of m-isometries
A bounded linear operator T on a Banach space X is called an (m,p)-isometry for a positive integer m and a real number p ≥ 1 if, for any vector x ∈ X, . We prove that any power of an (m,p)-isometry is also an (m,p)-isometry. In general the converse is not true. However, we prove that if and are (m,p)-isometries for a positive integer r, then T is an (m,p)-isometry. More precisely, if is an (m,p)-isometry and is an (l,p)-isometry, then is an (h,p)-isometry, where t = gcd(r,s) and h = min(m,l)....
Powers of operators
Powers of -hyponormal operators.
Practical Ulam-Hyers-Rassias stability for nonlinear equations
In this paper, we offer a new stability concept, practical Ulam-Hyers-Rassias stability, for nonlinear equations in Banach spaces, which consists in a restriction of Ulam-Hyers-Rassias stability to bounded subsets. We derive some interesting sufficient conditions on practical Ulam-Hyers-Rassias stability from a nonlinear functional analysis point of view. Our method is based on solving nonlinear equations via homotopy method together with Bihari inequality result. Then we consider nonlinear equations...
Preassigning eigenvalues and zeros of nuclear operators
Precise estimates on the rate at which certain diffusions tend to equilibrium.
Precompactness in the uniform ergodic theory
We characterize the Banach space operators T whose arithmetic means form a precompact set in the operator norm topology. This occurs if and only if the sequence is precompact and the point 1 is at most a simple pole of the resolvent of T. Equivalent geometric conditions are also obtained.
Preconditioners and Korovkin-type theorems for infinite-dimensional bounded linear operators via completely positive maps
The classical as well as noncommutative Korovkin-type theorems deal with the convergence of positive linear maps with respect to different modes of convergence, like norm or weak operator convergence etc. In this article, new versions of Korovkin-type theorems are proved using the notions of convergence induced by strong, weak and uniform eigenvalue clustering of matrix sequences with growing order. Such modes of convergence were originally considered for the special case of Toeplitz matrices and...
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p-representable operators in Banach spaces.
Preservation of ergodicity under perturbation.
Preservation of ergodicity under perturbation (Erratum).
Preservation of exponential stability for equations with several delays
We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays under the addition of new terms and a delay perturbation. We assume that the original equation has a positive fundamental function; our method is based on Bohl-Perron type theorems. Explicit stability conditions are obtained.