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Scalable frames in tensor product of Hilbert spaces
2020Tight frames are very similar to orthonormal bases and can be used as a good alternative to them. Scaling frames are introduced as a method to transform a general frame to a tight one. This paper investigates in under what conditions the tensor product of two frames is a scalable frame.
Zakeri, Samineh, Ahmadi, Ahmad
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Frame Operator and Hilbert-Schmidt Operator in Tensor Product of Hilbert Spaces
Journal of Dynamical Systems and Geometric Theories, 2009Abstract The tensor product of frames in Hilbert spaces is introduced. It was shown that the tensor product of two frames is a frame for the tensor product of Hilbert spaces. The concept of tensor frame operator on tensor product of Hilbert space is given and results of it are presented.
G. Upender Reddy +2 more
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Continuous tensor products of hilbert spaces and generalized random fields
Il Nuovo Cimento B Series 10, 1968The infinite tensor product is generalized to a tensor product of certain Hilbert spaces over a topological index set. The criterion for positivity of characteristic functionals of generalized random processes is used to construct two distinct types of continuous tensor products.
Streater, R. F., Wulfsohn, A.
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Tensor products of Hilbert space effect algebras
Reports on Mathematical Physics, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Gleason measures on infinite tensor products of Hilbert spaces
Journal of Mathematical Physics, 1977Nowak [Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 22, 393–5 (1974)] has given an example of a consistent (in the sense of Kolmogorov) family of Gleason measures [A. M. Gleason, J. Math. Mech. 6, 885–94 (1957)] {mn} defined over ⊗ni=1Hi which do not extend to a Gleason measure on ⊙∞i=1 ΦHi for a given construction of the infinite tensor product.
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Hilbert-Schmidt frames and Riesz bases with respect to tensor product of Hilbert spaces
Analysis MathematicaN.A. Jyoti, Lalit Kumar Vashisht
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Regular Functions of Operators on Tensor Products of Hilbert Spaces
Integral Equations and Operator Theory, 2005A class of linear operators on tensor products of Hilbert spaces is considered. Estimates for the norm of operator-valued functions regular on the spectrum are derived. These results are new even in the finite-dimensional case. By virtue of the obtained estimates, we derive stability conditions for semilinear differential equations. Applications of the
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Phase space methods in a continuous tensor product of Hilbert spaces
AIP Conference Proceedings, 2006A continuum of coupled oscillators is considered, described by a continuous tensor product of Hilbert spaces. The mode position Ux and the mode momentum Up are operators which act collectively on all oscillators. They obey equations of motion which are very similar to those of a harmonic oscillator.
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Tensor product of the octonionic Hilbert spaces and colour confinement
Journal of Physics A: Mathematical and General, 1978The definition of the tensor product of the octonionic Hilbert spaces with complex geometry is proposed. This definition is based on the isomorphism (geometric and algebraic) of the octonionic Hilbert space with appropriate structure. It is found that the algebraic colour confinement holds only partially.
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Observables and States in Tensor Products of Hilbert Spaces
1992Suppose (Ω i , F i ), 1 ≤ i ≤ n are sample spaces describing the elementary outcomes and events concerning n different statistical systems in classical probability. To integrate them into a unified picture under the umbrella of a single sample space one takes their cartesian product (Ω, F) where Ω = Ω1 x … x Ω n , F = F1 x … x F n , the smallest σ ...
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