Operators which respect norm intervals
Operators whose adjoints are quasi p-nuclear
For p ≥ 1, a set K in a Banach space X is said to be relatively p-compact if there exists a p-summable sequence (xₙ) in X with . We prove that an operator T: X → Y is p-compact (i.e., T maps bounded sets to relatively p-compact sets) iff T* is quasi p-nuclear. Further, we characterize p-summing operators as those operators whose adjoints map relatively compact sets to relatively p-compact sets.
Operators whose tensor powers are --continuous
Operators with absolute continuity properties: an application to quasinormality
An absolute continuity approach to quasinormality which relates the operator in question to the spectral measure of its modulus is developed. Algebraic characterizations of some classes of operators that emerge in this context are found. Various examples and counterexamples illustrating the concepts of the paper are constructed by using weighted shifts on directed trees. Generalizations of these results that cover the case of q-quasinormal operators are established.
Operators with Absolutely Bounded Matrices.
Operators with an ergodic power
We prove that if some power of an operator is ergodic, then the operator itself is ergodic. The converse is not true.
Operators with extension property and the principle of local reflexivity
Operators with hypercyclic Cesaro means
An operator T on a Banach space ℬ is said to be hypercyclic if there exists a vector x such that the orbit is dense in ℬ. Hypercyclicity is a strong kind of cyclicity which requires that the linear span of the orbit is dense in ℬ. If the arithmetic means of the orbit of x are dense in ℬ then the operator T is said to be Cesàro-hypercyclic. Apparently Cesàro-hypercyclicity is a strong version of hypercyclicity. We prove that an operator is Cesàro-hypercyclic if and only if there exists a vector...
Operators with rich invariant subspace lattices.
Operators with shift generating by a compact Lie group.
Operators with thin spectral sets.
Operator-splitting methods for general mixed variational inequalities.
Operator-valued analytic functions of constant norm
Operator-valued inner product and operator inequalities.
Operator-valued n-harmonic measure in the polydisc
An operator-valued multi-variable Poisson type integral is studied. In Section 2 we obtain a new equivalent condition for the existence of a so-called regular unitary dilation of an n-tuple T=(T₁,...,Tₙ) of commuting contractions. Our development in Section 2 also contains a new proof of the classical dilation result of S. Brehmer, B. Sz.-Nagy and I. Halperin. In Section 3 we turn to the boundary behavior of this operator-valued Poisson integral. The results obtained in this section improve upon...
Operator-Valued Ultradistributions in the Spectral Theory.
Opial's property and James' quasi-reflexive spaces
Two of James’ three quasi-reflexive spaces, as well as the James Tree, have the uniform -Opial property.
Optimal control of a frictionless contact problem with normal compliance
We consider a mathematical model which describes a contact between an elastic body and a foundation. The contact is frictionless with normal compliance. The goal of this paper is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. We state an optimal control problem which admits at least one solution. Next, we establish an optimality condition corresponding to a regularization...
Optimal control of nonlinear delay systems with implicit derivative and quadratic performance
The existence of optimal control for nonlinear delay systems having an implicit derivative with quadratic performance criteria is proved. The results are established by an iterative technique and using the Darbo fixed point theorem.
Optimal domains for kernel operators on [0,∞) × [0,∞)
Let T be a kernel operator with values in a rearrangement invariant Banach function space X on [0,∞) and defined over simple functions on [0,∞) of bounded support. We identify the optimal domain for T (still with values in X) in terms of interpolation spaces, under appropriate conditions on the kernel and the space X. The techniques used are based on the relation between linear operators and vector measures.