Systems of subspaces of a unitary space

Author(s)

Bondarenko, Vitalij M. ^[1] ; Futorny, Vyacheslav ^[2] ; Klimchuk, Tatiana ^[3] ; Sergeichuk, Vladimir V. ^[1] ; Yusenko, Kostyantyn ^{[2, 1]}

Affiliation

^[1] Ukrainian Acad Sci, Inst Math, Kiev - Ukraine

^[2] Univ Sao Paulo, Dept Math, BR-05508 Sao Paulo - Brazil

^[3] Kiev Natl Taras Shevchenko Univ, Fac Mech & Math, Kiev - Ukraine

• Document type: Journal article
• Source: Linear Algebra and its Applications; v. 438, n. 5, p. 2561-2573, MAR 1 2013.
• Web of Science Citations: 24

Abstract

For a finite poset P = [p(1),..., p(t)), we study systems (U-1,..., U-t)(U) of subspaces of a unitary space U such that U-i subset of U-j if p(i) < p(j). Two systems (U-1,..., U-t)(U) and (V-1,..., V-t)(V) are said to be isometric if there exists an isometry go : U -> V such that phi(U-i) = V-i. We classify such systems up to isometry if P is a semichain. We prove that the problem of their classification is unitarily wild if P is not a semichain. A classification problem is called unitarily wild if it contains the problem of classifying linear operators on a unitary space, which is hopeless in a certain sense. (C) 2012 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 10/50347-9 - Algebras, representations e applications
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 10/15781-0 - Stable vector bundles over projective plane and representations of posets in the category of unitary spaces
• Grantee: Kostiantyn Iusenko
• Support Opportunities: Scholarships in Brazil - Post-Doctoral