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Schreier singular operators
"... Abstract. In this paper we further investigate Schreier singular operators introduced in [ADST]. If X and Y are two Banach spaces, a bounded operator T: X → Y is Schreier singular if for every ε> 0 and every basic sequence (xn) in X there is a vector of the form x = ∑n i=1 aixk for some i a1,..., ..."
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Abstract. In this paper we further investigate Schreier singular operators introduced in [ADST]. If X and Y are two Banach spaces, a bounded operator T: X → Y is Schreier singular if for every ε> 0 and every basic sequence (xn) in X there is a vector of the form x = ∑n i=1 aixk for some i a1
On a progress in the theory of Lebesgue spaces with variable exponent: maximal and singular operators
 THE MAXIMAL OPERATOR 125
"... exponent: maximal and singular operators ..."
Singular Operators with Antisymmetric Kernels
 Related Capacities, and Wolff Potentials. Int. Math. Res. Notices
"... ar ..."
CLASSES OF STRICTLY SINGULAR OPERATORS AND THEIR PRODUCTS
, 2006
"... Abstract. V. D. Milman proved in [14] that the product of two strictly singular operators on Lp[0, 1] (1 � p < ∞) or on C[0, 1] is compact. In this note we utilize Schreier families Sξ in order to define the class of Sξstrictly singular operators, and then we refine the technique of Milman to sh ..."
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Cited by 8 (2 self)
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Abstract. V. D. Milman proved in [14] that the product of two strictly singular operators on Lp[0, 1] (1 � p < ∞) or on C[0, 1] is compact. In this note we utilize Schreier families Sξ in order to define the class of Sξstrictly singular operators, and then we refine the technique of Milman
A Singular Value Thresholding Algorithm for Matrix Completion
, 2008
"... This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task of reco ..."
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Cited by 555 (22 self)
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toimplement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank. The algorithm is iterative and produces a sequence of matrices {X k, Y k} and at each step, mainly performs a softthresholding operation on the singular values of the matrix Y k. There are two
Strictly singular operators and the invariant subspace problem
 Studia Math
, 1999
"... Properties of strictly singular operators have recently become of topical interest because the work of Gowers and Maurey in [GM1] and [GM2] gives (among many other brilliant and surprising results, such as [G1] and [G2]) Banach spaces on which every continuous operator is of form λI + S, where S is ..."
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Cited by 14 (0 self)
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Properties of strictly singular operators have recently become of topical interest because the work of Gowers and Maurey in [GM1] and [GM2] gives (among many other brilliant and surprising results, such as [G1] and [G2]) Banach spaces on which every continuous operator is of form λI + S, where
Powers of operators dominated by strictly singular operators
"... It is proved that every positive operator R on a Banach lattice E dominated by a strictly singular operator T: E → E satisfies that the R4 is strictly singular. Moreover, if E is order continuous then the R2 is already strictly singular. 1. ..."
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It is proved that every positive operator R on a Banach lattice E dominated by a strictly singular operator T: E → E satisfies that the R4 is strictly singular. Moreover, if E is order continuous then the R2 is already strictly singular. 1.
Multilinear singular operators with fractional rank
 Pacific J. Math
"... Abstract. We prove bounds for multilinear operators on R d given by multipliers which are singular along a k dimensional subspace. The new case of interest is when the rank k/d is not an integer. Connections with the concept of true complexity from Additive Combinatorics are also investigated. ..."
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Abstract. We prove bounds for multilinear operators on R d given by multipliers which are singular along a k dimensional subspace. The new case of interest is when the rank k/d is not an integer. Connections with the concept of true complexity from Additive Combinatorics are also investigated.
AN ORDINAL INDEX ON THE SPACE OF STRICTLY SINGULAR OPERATORS
, 2009
"... Using the notion of Sξstrictly singular operator introduced by Androulakis, Dodos, Sirotkin and Troitsky, we define an ordinal index on the subspace of strictly singular operators between two separable Banach spaces. In our main result, we provide a sufficient condition implying that this index is ..."
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Cited by 2 (2 self)
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Using the notion of Sξstrictly singular operator introduced by Androulakis, Dodos, Sirotkin and Troitsky, we define an ordinal index on the subspace of strictly singular operators between two separable Banach spaces. In our main result, we provide a sufficient condition implying that this index
Results 1  10
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4,111