scholarly journals A Schur type analysis of the minimal weak unitary Hilbert space dilations of a Kreĭn space bicontraction and the Relaxed Commutant Lifting Theorem in a Kreĭn space setting

2010 ◽  
Vol 259 (10) ◽  
pp. 2557-2586
Author(s):  
S.A.M. Marcantognini ◽  
M.D. Morán
Keyword(s):  
Hilbert Space ◽  
Krein Space ◽  
Type Analysis ◽  
Space Setting ◽  
Commutant Lifting ◽  
Kreĭn Space ◽  
Commutant Lifting Theorem

Some remarks on a paper by W. N. Everitt

1977 ◽  
Vol 78 (1-2) ◽  
pp. 71-79 ◽  
Author(s):  
K. Daho ◽  
H. Langer
Keyword(s):  
Hilbert Space ◽  
Weight Function ◽  
Selfadjoint Operator ◽  
Krein Space ◽  
Indefinite Weight ◽  
Indefinite Weight Function ◽  
Kreĭn Space ◽  
Pontrjagin Space

Everitt has shown [1[, that for α ∊ [0, π/2] the undernoted problem (1.1–2) with an indefinite weight function r can be represented by a selfadjoint operator in a suitable Hilbert space. This result is extended to arbitrary α ∊ [0, π), replacing the Hilbert space in some cases by a Pontrjagin space with index one. The problem is also treated in the Krein space generated by the weight function r.

Vacuum polarization of weak interaction theory in Krein space quantization

2019 ◽  
Vol 34 (07n08) ◽  
pp. 1950050
Author(s):  
B. Forghan
Keyword(s):  
Hilbert Space ◽  
Weak Interaction ◽  
Regularization Method ◽  
Vacuum Polarization ◽  
Krein Space ◽  
Dimensional Regularization ◽  
Interaction Theory ◽  
Kreĭn Space ◽  
Krein Space Quantization

In this paper, one of the most important diagrams of weak interaction (vacuum polarization) is studied in Krein space quantization (KSQ). This diagram has divergent terms in Hilbert space which must be eliminated using a traditional regularization method like dimensional regularization whereas in KSQ the result is automatically finite and does not need renormalization.

On Operators with Spectral Square but without Resolvent Points

2005 ◽  
Vol 57 (1) ◽  
pp. 61-81 ◽  
Author(s):  
Paul Binding ◽  
Vladimir Strauss
Keyword(s):  
Hilbert Space ◽  
Spectral Type ◽  
Krein Space ◽  
Resolvent Set ◽  
Hilbert Space Operators ◽  
Kreĭn Space

AbstractDecompositions of spectral type are obtained for closed Hilbert space operators with empty resolvent set, but whose square has closure which is spectral. Krein space situations are also discussed.

scholarly journals A class of linear kinetic equations in a Krein space setting

1988 ◽  
Vol 11 (4) ◽  
pp. 518-535 ◽  
Author(s):  
Alexander H. Ganchev ◽  
William Greenberg ◽  
C. V. M. van der Mee
Keyword(s):  
Krein Space ◽  
Kinetic Equations ◽  
Space Setting ◽  
Kreĭn Space ◽  
Linear Kinetic

scholarly journals Weyl type theorems for selfadjoint operators on Krein spaces

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 6001-6016
Author(s):  
Il An ◽  
Jaeseong Heo
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Krein Space ◽  
Linear Operators ◽  
Fredholm Theory ◽  
Bounded Linear ◽  
Selfadjoint Operators ◽  
Krein Spaces ◽  
Weyl Type Theorems ◽  
Kreĭn Space

In this paper, we introduce a notion of the J-kernel of a bounded linear operator on a Krein space and study the J-Fredholm theory for Krein space operators. Using J-Fredholm theory, we discuss when (a-)J-Weyl?s theorem or (a-)J-Browder?s theorem holds for bounded linear operators on a Krein space instead of a Hilbert space.

H-infinity deconvolution filtering: a Krein space approach in state-space setting

2009 ◽  
Vol 7 (2) ◽  
pp. 185-191 ◽  
Author(s):  
Xiao Lu ◽  
Huanshui Zhang ◽  
Wei Wang ◽  
Jie Yan
Keyword(s):  
State Space ◽  
Krein Space ◽  
H Infinity ◽  
Space Setting ◽  
Kreĭn Space ◽  
Space Approach

scholarly journals Computing the numerical range of Krein space operators

2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Natalia Bebiano ◽  
J. da Providência ◽  
A. Nata ◽  
J.P. da Providência
Keyword(s):  
Hilbert Space ◽  
Quadratic Form ◽  
Numerical Range ◽  
Krein Space ◽  
Inner Product ◽  
Indefinite Inner Product ◽  
Finite Dimensional ◽  
Alternative Algorithm ◽  
Kreĭn Space ◽  
Finite Dimensional Case

Abstract Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their easily determined elliptical and hyperbolical numerical ranges. The numerical results reported here indicate that this method is very efficient, since it is faster and more accurate than either of the existing algorithms. Further, it may yield easy solutions for the inverse indefinite numerical range problem. Our algorithm uses an idea of Marcus and Pesce from 1987 for generating Hilbert space numerical ranges of matrices of size n.

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