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Decomposability and local spectral properties of a normal linear relation
Our objective in this paper is to show that, similarly to the case of normal operators, a normal linear relation on a Hilbert space H satisfies...
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Maximally Аccretive and Nonnegative Extensions of a Nonnegative Linear Relation
In terms of spaces of boundary values, we formulate and prove criteria of maximal θ-accretivity and maximal nonnegativity for the proper extension of...
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An Index Theorem for Linear Relations and Its Applications to the Study of Block Relation Matrices
AbstractIn this paper, we aim to prove an index theorem for linear relations and apply it to study the invertibility and the essential invertibility...
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Invariance of the essential spectra of closed linear operator pencils on a Banach space
In this paper, we detail some results of the essential spectra of closed linear operators pencils defined on a Banach space X . This is done by...
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Multiply Closed Control Strategy in a Linear Terminal Problem of Optimal Guaranteed Control
This paper deals with an optimal control problem for a linear discrete system with disturbances. It is required to steer the system robustly to a...
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Periodic linear groups in which permutability is a transitive relation
A PT -group is a group in which the relation of being a permutable subgroup is transitive. The main aim of this paper is to show that a (homomorphic...
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Relationships between inessential, strictly singular, strictly cosingular and improjective linear relations
This paper is devoted to study the interrelations between inessential, improjective, strictly singular and strictly cosingular linear relations....
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On Perturbation of Drazin Invertible Linear Relations
We study the problem of stability of regular, finite ascent, and finite descent linear relations defined in Banach spaces under commuting nilpotent...
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Closed Meromorphic 1-Forms
We review properties of closed meromorphic 1-forms and of the foliations defined by them. We present and explain classical results from foliation...
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The Krein transform and semi-bounded extensions of semi-bounded linear relations
The Krein transform is the real counterpart of the Cayley transform and gives a one-to-one correspondence between the positive relations and...
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Pseudo Algebraically Closed Fields
By Hilbert’s Nullstellensatz, algebraically closed fields are PAC. So are separably closed fields [Lan64, p. 76, Prop. 10]. Both statements are also...
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Partial isometries and generalized inverses of linear relations
For a closed linear relation everywhere defined on a Hilbert space the concepts of isometry, co-isometry, partial isometry, and generalized inverse...
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Algebraically Closed Fields
We establish a simple algebraic elimination of quantifiers procedure for the theory of algebraically closed fields. This theory is model complete...
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On the essential minimum and essential surjectivity moduli of linear relations in Banach spaces
For a closed linear relation everywhere defined and acting between two Banach spaces the concepts of essential minimum modulus and essential...
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The index of a linear relation under strictly singular perturbations
In this paper, we investigate the behaviour of the index of upper and lower semi-Fredholm multivalued linear operators in Banach spaces under...
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Sharp Simons type integral inequalities for closed linear Weingarten submanifolds in a space form
We prove sharp Simons type integral inequalities for n -dimensional closed linear Weingarten submanifolds (that is, submanifolds whose scalar and mean...