scholarly journals Spectral Order Automorphisms on Hilbert Space Effects and Observables: The 2-Dimensional Case

2016 ◽  
Vol 106 (4) ◽  
pp. 535-544 ◽  
Author(s):  
Lajos Molnár ◽  
Gergő Nagy
Keyword(s):  
Hilbert Space ◽  
Dimensional Case ◽  
Spectral Order ◽  
Hilbert Space Effects ◽  
Space Effects

A note on the infimum problem of Hilbert space effects

2006 ◽  
Vol 47 (10) ◽  
pp. 102103 ◽  
Author(s):  
Li Yuan ◽  
Hong-Ke Du
Keyword(s):  
Hilbert Space ◽  
Hilbert Space Effects ◽  
Space Effects

Preserving some numerical correspondencesbetween Hilbert space effects

2004 ◽  
Vol 54 (2) ◽  
pp. 201-209 ◽  
Author(s):  
Endre Kovács ◽  
Lajos Molnár
Keyword(s):  
Hilbert Space ◽  
Hilbert Space Effects ◽  
Space Effects

scholarly journals Infima of Hilbert space effects

1999 ◽  
Vol 286 (1-3) ◽  
pp. 1-17 ◽  
Author(s):  
T. Moreland ◽  
S. Gudder
Keyword(s):  
Hilbert Space ◽  
Hilbert Space Effects ◽  
Space Effects

scholarly journals Preservers on Hilbert space effects

2003 ◽  
Vol 370 ◽  
pp. 287-300 ◽  
Author(s):  
Lajos Molnár
Keyword(s):  
Hilbert Space ◽  
Hilbert Space Effects ◽  
Space Effects

On the infimum problem of Hilbert space effects

2006 ◽  
Vol 49 (4) ◽  
pp. 545-556 ◽  
Author(s):  
Hongke Du ◽  
Chunyuan Deng ◽  
Qihui Li
Keyword(s):  
Hilbert Space ◽  
Hilbert Space Effects ◽  
Space Effects

scholarly journals A new proof of Donoghue's interpolation theorem

2004 ◽  
Vol 2 (3) ◽  
pp. 253-265 ◽  
Author(s):  
Yacin Ameur
Keyword(s):  
Hilbert Space ◽  
Radon Measure ◽  
Interpolation Theorem ◽  
Dimensional Case ◽  
Infinite Dimensional ◽  
Positive Radon Measure ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
New Interpretation ◽  
Necessary And Sufficient

We give a new proof and new interpretation of Donoghue's interpolation theorem; for an intermediate Hilbert spaceH∗to be exact interpolation with respect to a regular Hilbert coupleH¯it is necessary and sufficient that the norm inH∗be representable in the form‖f‖∗=(∫[0,∞](1+t−1)K2(t,f;H¯)2dρ(t))1/2with some positive Radon measureρon the compactified half-line[0,∞]. The result was re-proved in [1] in the finite-dimensional case. The purpose of this note is to extend the proof given in [1] to cover the infinite-dimensional case. Moreover, the presentation of the aforementioned proof in [1] was slightly flawed, because we forgot to include a reference to ‘Donoghue's Lemma’, which is implicitly used in the proof. Hence we take this opportunity to correct that flaw.

scholarly journals Complementary Lagrangians in infinite dimensional symplectic Hilbert spaces

2005 ◽  
Vol 77 (4) ◽  
pp. 589-594 ◽  
Author(s):  
Paolo Piccione ◽  
Daniel V. Tausk
Keyword(s):  
Hilbert Space ◽  
Hilbert Spaces ◽  
Countable Family ◽  
Spectral Theorem ◽  
Dimensional Case ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Lagrangian Subspaces ◽  
Finite Dimensional Case ◽  
Adjoint Operators

We prove that any countable family of Lagrangian subspaces of a symplectic Hilbert space admits a common complementary Lagrangian. The proof of this puzzling result, which is not totally elementary also in the finite dimensional case, is obtained as an application of the spectral theorem for unbounded self-adjoint operators.

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