Results 1 to 10 of about 68 (27)
Trace-Class and Nuclear Operators
Concrete Operators, 2022 This paper explores the long journey from projective tensor products of a pair of Banach spaces, passing through the definition of nuclear operators still on the realm of projective tensor products, to the of notion of trace-class operators on a Hilbert ...
Kubrusly Carlos S.
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Concrete Operators, 2023 Given Banach space operators Si{S}_{i} and Ti{T}_{i}, i=1,2i=1,2, we use elementary properties of the left and right multiplication operators to prove, that if the tensor products pair (S1⊗S2,T1⊗T2)\left({S}_{1}\otimes {S}_{2},{T}_{1}\otimes {T}_{2}) is ...
Duggal Bhagawati Prashad, Kim In Hyoun
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m-isometric generalised derivations
Concrete Operators, 2022 Given Banach space operators Ai, Bi (i = 1, 2), let δi denote (the generalised derivation) δi(X) = (LAi − RBi )(X) = AiX − XBi. If 0 ∈ σa(Bi), i = 1, 2, and if Δδ1,δ2n(I)=(Lδ1Rδ1-I)n(I)=0\Delta _{{\delta _1},\delta 2}^n\left( I \right) = {\left( {{L_ ...
Duggal B.P., Kim I.H.
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Structure of n-quasi left m-invertible and related classes of operators
Demonstratio Mathematica, 2020 Given Hilbert space operators T,S∈B(ℋ)T,S\in B( {\mathcal H} ), let Δ\text{Δ} and δ∈B(B(ℋ))\delta \in B(B( {\mathcal H} )) denote the elementary operators ΔT,S(X)=(LTRS−I)(X)=TXS−X{\text{Δ}}_{T,S}(X)=({L}_{T}{R}_{S}-I)(X)=TXS-X and δT,S(X)=(
Duggal Bhagwati Prashad, Kim In Hyun
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Additivity violation of the regularized minimum output entropy [PDF]
, 2022 The problem of additivity of the Minimum Output Entropy is of fundamental importance in Quantum Information Theory (QIT). It was solved by textit{Matthew B. Hastings} [``Superadditivity of communication capacity using entangled inputs'', Nature Physics 5,
Collins, Benoît, Youn, Sang-Gyun
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Convenient Tail Bounds for Sums of Random Tensors [PDF]
, 2022 This work prepares new probability bounds for sums of random, inde-pendent, Hermitian tensors. These probability bounds characterize large-deviation behavior of the extreme eigenvalue of the sums of random tensors.
Chang, Shih Yu, Lin, Wen Wei
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On $(n,k)$-quasi class $Q$ Operators [PDF]
, 2020 Let $T$ be a bounded linear operator on a complex Hilbert space $H$. In this paper we introduce a new class of operators: $(n,k)$-quasi class $Q$ operators, superclass of $(n,k)$-quasi paranormal operators.
Braha, Naim L., Hoxha, Ilmi
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Matrices with multiplicative entries are tensor products [PDF]
, 2017 We study operators which have (infinite) matrix representation whose entries are multiplicative functions of two variables. We show that such operators are infinite tensor products over the primes.
Berberian +19 more
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Natural symmetric tensor norms [PDF]
, 2012 In the spirit of the work of Grothendieck, we introduce and study natural symmetric n-fold tensor norms. These are norms obtained from the projective norm by some natural operations.
Carando, Daniel Germán +1 more
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Operator Positivity and Analytic Models of Commuting Tuples of Operators
, 2016 We study analytic models of operators of class $C_{\cdot 0}$ with natural positivity assumptions. In particular, we prove that for an $m$-hypercontraction $T \in C_{\cdot 0}$ on a Hilbert space $\mathcal{H}$, there exists a Hilbert space $\mathcal{E ...
Bhattacharjee, Monojit, Sarkar, Jaydeb
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