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of 165
pro vyhledávání: '"47a80"'
The multiparameter matrix pencil problem (MPP) is a generalization of the one-parameter MPP: given a set of $m\times n$ complex matrices $A_0,\ldots, A_r$, with $m\ge n+r-1$, it is required to find all complex scalars $\lambda_0,\ldots,\lambda_r$, no
Externí odkaz:
http://arxiv.org/abs/2406.17879
We establish a central limit theorem for tensor product random variables $c_k:=a_k \otimes a_k$, where $(a_k)_{k \in \mathbb{N}}$ is a free family of variables. We show that if the variables $a_k$ are centered, the limiting law is the semi-circle. Ot
Externí odkaz:
http://arxiv.org/abs/2404.19662
Autor:
Majumdar, Arup, Johnson, P. Sam
This paper delves into several characterizations of $A$-approximate point spectrum of A-bounded operators acting on a complex semi-Hilbertian space $H$ and also investigates properties of the $A$-approximate point spectrum for the tensor product of t
Externí odkaz:
http://arxiv.org/abs/2403.05071
Autor:
Majumdar, Arup, Johnson, P. Sam
In this paper, we prove the relation $\frac{r_{A}(T) + r_{A}(T^{\diamond}) + |r_{A}(T^{\diamond}) - r_{A}(T)|}{2} = \sup \{ |\lambda|: \lambda \in \sigma_{A}(T)\}$, where $A$ is a positive semidefinite operator (not necessarily to have a closed range
Externí odkaz:
http://arxiv.org/abs/2402.12961
Publikováno v:
Complex Anal. Oper. Theory 18, 75 (2024)
Using the Wold-von Neumann decomposition for the isometric covariant representations due to Muhly and Solel, we prove an explicit representation of the commutant of a doubly commuting pure isometric representation of the product system over $\mathbb{
Externí odkaz:
http://arxiv.org/abs/2308.16674
Autor:
Pasqualetto, Enrico
We study projective and injective tensor products of Banach $L^0$-modules over a $\sigma$-finite measure space. En route, we extend to Banach $L^0$-modules several technical tools of independent interest, such as quotient operators, summable families
Externí odkaz:
http://arxiv.org/abs/2308.03634
Autor:
Turnansky, Morrison
We introduce a new structure, the critical multi-cubic lattice. Notably the critical multi-cubic lattice is the first true generalization of the cubic lattice to higher dimensional spaces. We then introduce the notion of a homomorphism in the categor
Externí odkaz:
http://arxiv.org/abs/2306.12236
Autor:
Turnansky, Morrison
In quantum mechanics, the connection between the operator algebraic realization and the logical models of measurement of state observables has long been an open question. In the approach that is presented here, we introduce a new application of the c
Externí odkaz:
http://arxiv.org/abs/2306.05903
Publikováno v:
Open Mathematics, Vol 22, Iss 1, Pp 212-244 (2024)
We consider the tensor products of square matrices of different sizes and introduce the stretching maps, which can be viewed as a generalized matricization. Stretching maps conserve algebraic properties of the tensor product, but are not necessarily
Externí odkaz:
https://doaj.org/article/f6793547b71d4e5aab1a1101d28954ec
Autor:
Stengl, Marian
In this paper an alternative version of the quantum phase estimation is proposed, in which the Hadamard gates at the beginning are substituted by a quantum Fourier transform. This new circuit coincides with the original one, when the ancilla is initi
Externí odkaz:
http://arxiv.org/abs/2303.05894