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Journal of Mathematical Analysis and Applications, 2020
The notion of two-Lipschitz operator arises as a natural extension of the idea of Lipschitz operator from \(X\) (a metric space) to \(E\) (a Banach space) to operators defined on \(X \times Y\) (\(X\) and \(Y\) being metric spaces) and taking values on \(E\). As usual, it is assumed that \(X\) and \(Y\) have each a distinguished point (both denoted by \
Hamidi, Khaled +3 more
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The notion of two-Lipschitz operator arises as a natural extension of the idea of Lipschitz operator from \(X\) (a metric space) to \(E\) (a Banach space) to operators defined on \(X \times Y\) (\(X\) and \(Y\) being metric spaces) and taking values on \(E\). As usual, it is assumed that \(X\) and \(Y\) have each a distinguished point (both denoted by \
Hamidi, Khaled +3 more
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, 2021
We study the sequence space X p q obtained by using the domain of q-analogue of the Cesaro matrix C ( q ) = ( c i j q ) defined by c i j q = { q j − 1 [ i ] q ( 1 ≤ j ≤ i ) , 0 ( j > i ) , where the notation [ i ] q has the usual meaning.
Taja Yaying, B. Hazarika, M. Mursaleen
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We study the sequence space X p q obtained by using the domain of q-analogue of the Cesaro matrix C ( q ) = ( c i j q ) defined by c i j q = { q j − 1 [ i ] q ( 1 ≤ j ≤ i ) , 0 ( j > i ) , where the notation [ i ] q has the usual meaning.
Taja Yaying, B. Hazarika, M. Mursaleen
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There is no largest proper operator ideal
Mathematische Annalen, 2020An operator ideal is proper if the only invertible operators it contains have finite rank. We answer a problem posed by Pietsch (Operator ideals, North-Holland, Amsterdam, 1980) by proving (i) that the ideal of inessential operators is not maximal among ...
V. Ferenczi
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Summability of sequences and extensions of operator ideals
Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2022Given a Banach space Y, the so-called right Y and left Y-extensions of operator ideals are introduced and applied to the study of operator ideal properties of well-known classes of operators on Banach spaces.
J. Fourie, E. D. Zeekoei
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Positivity, 2003
Let \(E, F\) be Riesz spaces. \(T: E \to F\) is called an ideal (inverse ideal) operator if \(T (I) (T^{-1} (J))\) is an order ideal in \(E (F)\) for each order ideal \(I (J)\) in \(E (F)\). It is shown that these operators can be characterized by their action on principal order ideals.
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Let \(E, F\) be Riesz spaces. \(T: E \to F\) is called an ideal (inverse ideal) operator if \(T (I) (T^{-1} (J))\) is an order ideal in \(E (F)\) for each order ideal \(I (J)\) in \(E (F)\). It is shown that these operators can be characterized by their action on principal order ideals.
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Every Banach ideal of polynomials is compatible with an operator ideal
, 2010We show that for each Banach ideal of homogeneous polynomials, there exists a (necessarily unique) Banach operator ideal compatible with it. Analogously, we prove that any ideal of n-homogeneous polynomials belongs to a coherent sequence of ideals of k ...
D. Carando +2 more
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Science Robotics, 2019
A bilateral teleoperation system facilitates locomotion synchronization of a human operator and a small bipedal robot. Despite remarkable progress in artificial intelligence, autonomous humanoid robots are still far from matching human-level manipulation
João Ramos, Sangbae Kim
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A bilateral teleoperation system facilitates locomotion synchronization of a human operator and a small bipedal robot. Despite remarkable progress in artificial intelligence, autonomous humanoid robots are still far from matching human-level manipulation
João Ramos, Sangbae Kim
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Some Operator Ideal Properties of Volterra Operators on Bergman and Bloch Spaces
Integral equations and operator theory, 2023Joelle Jreis, P. Lefèvre
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Representation of sequence classes by operator ideals
Journal of Mathematical Analysis and ApplicationsIt is well known that weakly $p$-summable sequences in a Banach space $E$ are associated to bounded operators from $\ell_{p^*}$ to $E$, and unconditionally $p$-summable sequences in $E$ are associated to compact operators from $\ell_{p^*}$ to $E ...
Geraldo Botelho, Ariel S. Santiago
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Unusual Traces on Operator Ideals
Mathematische Nachrichten, 1987Let H be a separable Hilbert space and B(H) (resp. \(B_ 0(H))\) the space of all bounded linear operators (resp. compact operators) defined on H. Given an ideal J in \(B_ 0(H)\) a trace on J is a linear functional \(\tau\) on J so that (1) \(\tau (P)=1\) if P is a rank one projection, (2) \(\tau (XY)=\tau (YX)\) if \(X\in J\) and \(Y\in B(H).\) We say ...
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