Demicompact and k-D-Set-contractive Multivalued Linear Operators
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DOI: 10.1007/s00009-018-1078-z
Abstract: In this paper, we extend the concept of demicompactness and k-set-contractive linear operators on multivalued linear operators and we develop some properties. Finally, we establish a rapport with the theory of fixed points. read more here.
Keywords: multivalued linear; demicompact set; set contractive; linear operators ... See more keywords
Power Series of Positive Linear Operators
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DOI: 10.1007/s00009-019-1313-2
Abstract: We describe a unifying approach for studying the power series of the positive linear operators from a certain class. For the same operators, we give simpler proofs of some known ergodic theorems. read more here.
Keywords: positive linear; power series; linear operators; series positive ... See more keywords
Orthogonalities, linear operators, and characterization of inner product spaces
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DOI: 10.1007/s00010-017-0494-7
Abstract: It is proved that a normed space, whose dimension is at least three, admitting a nonzero linear operator reversing Birkhoff orthogonality is an inner product space, which releases the smoothness condition in one of J.… read more here.
Keywords: product spaces; product; inner product; orthogonalities linear ... See more keywords
On linear operators preserving certain cones in $$\mathbb {R}^n$$Rn
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DOI: 10.1007/s11117-019-00675-3
Abstract: A distinguished class of polyhedral cones is considered. For a linear operator $$\mathcal {L}$$L preserving a cone in this class, we prove, under some assumption on the number of edges of the cone, that its… read more here.
Keywords: preserving certain; certain cones; linear operators; operators preserving ... See more keywords
Perturbation of unbounded linear operators by $$\gamma $$γ-relative boundedness
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DOI: 10.1007/s11587-017-0341-0
Abstract: Diagana (Handbook on operator theory. Springer, Basel, pp 875–880, 2015) studied some sufficient conditions such that if S, T and K are three unbounded linear operators with S being a closed operator, then their algebraic sum $$S+T+K$$S+T+K is… read more here.
Keywords: relative boundedness; unbounded linear; operator; linear operators ... See more keywords
Some generalizations of ascent and descent for linear operators
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DOI: 10.1007/s40065-021-00328-y
Abstract: The purpose of this paper is to present in linear spaces some results for new notions called A-left (resp., A-right) ascent and A-left (resp., A-right) descent of linear operators (where A is a given operator)… read more here.
Keywords: linear operators; generalizations ascent; descent linear; ascent descent ... See more keywords
A study of orthogonality of bounded linear operators
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DOI: 10.1007/s43037-019-00050-0
Abstract: We study Birkhoff-James orthogonality and isosceles orthogonality of bounded linear operators between Hilbert spaces and Banach spaces. We explore Birkhoff-James orthogonality of bounded linear operators in light of a new notion introduced by us and… read more here.
Keywords: linear operators; bounded linear; orthogonality bounded; birkhoff james ... See more keywords
Dynamics of generalized hyperbolic linear operators
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DOI: 10.1016/j.aim.2021.107830
Abstract: Abstract It is introduced an open class of linear operators on Banach spaces such that their non-wandering set is an infinite dimensional topologically mixing subspace, where the periodic points are dense (in particular, they are… read more here.
Keywords: wandering set; generalized hyperbolic; linear operators; non wandering ... See more keywords
Numerical radius attaining compact linear operators
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DOI: 10.1016/j.jmaa.2016.02.074
Abstract: Abstract We show that there are compact linear operators on Banach spaces which cannot be approximated by numerical radius attaining operators. read more here.
Keywords: compact linear; radius attaining; numerical radius; attaining compact ... See more keywords
Local solvability for a class of linear operators in Besov and Hölder spaces
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DOI: 10.1016/j.jmaa.2018.04.077
Abstract: Abstract We show local solvability in Besov spaces for a class of first order linear operators L defined on an open set of R n + 1 , n ∈ N , satisfying the condition… read more here.
Keywords: local solvability; solvability; solvability class; linear operators ... See more keywords
Adiabatic theorems for general linear operators with time-independent domains
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DOI: 10.1142/s0129055x19500144
Abstract: We establish adiabatic theorems with and without spectral gap conditions for general — typically dissipative — linear operators [Formula: see text] with time-independent domains [Formula: see text] in some Banach space [Formula: see text]. Compared… read more here.
Keywords: linear operators; time independent; formula see; adiabatic theorems ... See more keywords