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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Systems of subspaces in Hilbert space that obey certain conditions, on their pairwise angles


Authors: A. V. Strelets and I. S. Feshchenko
Translated by: S. Kislyakov
Original publication: Algebra i Analiz, tom 24 (2012), nomer 5.
Journal: St. Petersburg Math. J. 24 (2013), 823-846
MSC (2010): Primary 46C05
Published electronically: July 24, 2013
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Abstract: The paper is devoted to systems of subspaces $ H_{1},\dots ,H_{n}$ of a complex Hilbert space $ H$ that satisfy the following conditions: for every index $ i>1$, the angle $ \theta _{1,i}\in (0,\pi /2)$ between $ H_{1}$ and $ H_{i}$ is fixed; the projections onto $ H_{2k}$ and $ H_{2k+1}$ commute for $ 1\leq k\leq m$ ($ m$ is a fixed nonnegative number satisfying $ m\leq (n-1)/2$); all other pairs $ H_{i}$, $ H_{j}$ are orthogonal. The main tool in the study is a construction of a system of subspaces in a Hilbert space on the basis of its Gram operator (the $ G$-construction).


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Additional Information

A. V. Strelets
Affiliation: Division of functional analysis, Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkovskaya ul. 3, Kiev 01061, Ukraine
Email: alexander.strelets@gmail.com

I. S. Feshchenko
Affiliation: Department of Mechanics and Mathematics, Taras Shevchenko National University of Kiev, Academician Glushkov prospect 4e, Kiev, Ukraine
Email: ivanmath007@gmail.com

DOI: http://dx.doi.org/10.1090/S1061-0022-2013-01264-7
PII: S 1061-0022(2013)01264-7
Keywords: System of subspaces, Hilbert space, orthogonal projection, Gram operator
Received by editor(s): January 28, 2012
Published electronically: July 24, 2013
Article copyright: © Copyright 2013 American Mathematical Society