Results 91 to 100 of about 6,185,996 (263)
On operator inequalities and linear combinations of operators
Linear Algebra and its Applications, 1991 AbstractLet A1,…,Ak,C,PϵB(H), the Banach algebra of all bounded linear operators on a complex Hilbert space H. It is shown that (1) A1PA∗1+⋯+AkPA∗ k⩾CPC∗ for all P⩾0 if and only if for every x in H there exist scalars a1(x),…,ak(x) with |a1(x)|2+⋯+|ak(x)|2⩽1 such that Cx=a1(x)A1x+⋯+ak(x)Akx; (2) A1PA∗1+A2PA∗2⩾CPC∗ for all P⩾0 if and only if C=aA1 +bA2 ...
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Some remarks on distributional chaos for bounded linear operators
, 2015 The aim of this paper is to study distributional chaos for bounded linear operators. We show that distributional chaos of type k \in {1,2} is an invariant of topological conjugacy between two bounded linear operators.
Lvlin Luo, B. Hou
semanticscholar +1 more source
Tractability of Multivariate Problems for Standard and Linear Information in the Worst Case Setting: Part I [PDF]
arXiv, 2015 We present a lower error bound for approximating linear multivariate operators defined over Hilbert spaces in terms of the error bounds for appropriately constructed linear functionals as long as algorithms use function values. Furthermore, some of these linear functionals have the same norm as the linear operators.
arxiv
A certain class of linear operators
Journal of Numerical Analysis and Approximation Theory, 1997 Not available.
Emil C. Popa
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Density Invariance of Certain Operational Quantities of Bounded Linear Operators in Normed Spaces [PDF]
arXiv, 2001 Based on ideas of R.W. Cross, a simplified proof is presented of the density invariance of certain operational quantities associated with bounded linear operators in normed vector spaces.
arxiv
Distributional chaos for linear operators
Journal of Functional Analysis, 2013 We characterize distributional chaos for linear operators on Fréchet spaces in terms of a computable condition (DCC), and also as the existence of distributionally irregular vectors. A sufficient condition for the existence of dense uniformly distributionally irregular manifolds is presented, which is very general and can be applied to many classes of ...
Bernardes, Nilson C. +3 more
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Boundedness and closedness of linear relations [PDF]
arXiv, 2016 This paper studies boundedness and closedness of linear relations, which include both single-valued and multi-valued linear operators. A new (single-valued) linear operator induced by a linear relation is introduced, and its relationships with other two important induced linear operators are established.
arxiv
Neural Networks as Positive Linear Operators
MathematicsBasic neural network operators are interpreted as positive linear operators and the related general theory applies to them. These operators are induced by a symmetrized density function deriving from the parametrized and deformed hyperbolic tangent ...
George A. Anastassiou
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Lomonosov's Invariant Subspace Theorem for Multivalued Linear Operators [PDF]
Proc. Amer. Math. Soc. 131 (2003), 825-834, 2000 The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E "commutes" with a compact nonzero operator K, i.e., TK=KT, then T has a non-trivial closed invariant subspace. We generalize this theorem for multivalued linear operators.
arxiv