A characterization of some subsets of S-essential spectra of a multivalued linear operator
We characterize some S-essential spectra of a closed linear relation in terms of certain linear relations of semi-Fredholm type.
A new theorem on exponential stability of periodic evolution families on Banach spaces.
Browder Riesz-Schauder theory for polynomially finite rank linear relations
We describe the Browder Riesz-Schauder theory of compact operators in Banach spaces in the context of polynomially finite rank linear relations in Banach spaces.
Characterisations of open multivalued linear operators
The class of all open linear relations is characterised in terms of the restrictions of the linear relations to finite-codimensional subspaces. As an application, we establish two results, the first of which shows that an upper semi-Fredholm linear relation retains its index under finite rank perturbations, and the second is a density theorem for lower bounded linear relations that have closed range. Results of Labuschagne and of Mbekhta about linear operators are covered.
Characterizations of nonnegative selfadjoint extensions.
Componentwise and Cartesian decompositions of linear relations [Book]
Concave iteration semigroups of linear set-valued functions
We consider a concave iteration semigroup of linear continuous set-valued functions defined on a closed convex cone in a separable Banach space. We prove that such an iteration semigroup has a selection which is also an iteration semigroup of linear continuous functions. Moreover it is majorized by an "exponential" family of linear continuous set-valued functions.
Erratum to "Stability of the index of a linear relation under compact perturbations" (Studia Math. 180 (2007), 95-102)
We give a corrected version of the main result from the paper cited in the title. We obtain necessary and sufficient conditions for the stability of the topological index of an open linear relation under compact perturbations
Essential self-adjointness of symmetric linear relations associated to first order systems
The purpose of this note is to present several criteria for essential self-adjointness. The method is based on ideas due to Shubin. This note is divided into two parts. The first part deals with symmetric first order systems on the line in the most general setting. Such a symmetric first order system of differential equations gives rise naturally to a symmetric linear relation in a Hilbert space. In this case even regularity is nontrivial. We will announce a regularity result and discuss criteria...
Multivalued linear operators and differential inclusions in Banach spaces
In this paper, we study multivalued linear operators (MLO's) and their resolvents in non reflexive Banach spaces, introducing a new condition of a minimal growth at infinity, more general than the Hille-Yosida condition. Then we describe the generalized semigroups induced by MLO's. We present a criterion for an MLO to be a generator of a generalized semigroup in an arbitrary Banach space. Finally, we obtain some existence results for differential inclusions with MLO's and various types of multivalued...
On the Fredholm alternative for the Fučík spectrum.
On the Krall-type polynomials.
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...
Stability of the index of a linear relation under compact perturbations
We prove the stability under compact perturbations of the algebraic index of a Fredholm linear relation with closed range acting between normed spaces. Our main tool is a result concerning the stability of the index of a complex of Banach spaces under compact perturbations.
The Cauchy problem for an inclusion in Banach spaces and distribution spaces.
The conjugate of a product of linear relations
Let , and be normed linear spaces with and linear relations, i.e. setvalued maps. We seek necessary and sufficient conditions that would ensure that . First, we cast the concepts of relative boundedness and co-continuity in the set valued case and establish a duality. This duality turns out to be similar to the one that exists for densely defined linear operators and is then used to establish the necessary and sufficient conditions. These conditions are similar to those for the single...