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ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 676835, 16 pages
http://dx.doi.org/10.5402/2012/676835
Research Article

The Theory for 𝐽-Hermitian Subspaces in a Product Space

Department of Mathematics, Shandong University at Weihai, Weihai, Shandong 264209, China

Received 6 January 2012; Accepted 13 February 2012

Academic Editors: S. Deng and O. Miyagaki

Copyright Β© 2012 Huaqing Sun and Jiangang Qi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the theory for 𝐽-Hermitian subspaces. The defect index of a 𝐽-Hermitian subspace is defined, and a formula for the defect index is established; the result that every 𝐽-Hermitian subspace has a 𝐽-self-adjoint subspace extension is obtained; all the 𝐽-self-adjoint subspace extensions of a 𝐽-Hermitian subspace are characterized. This theory will provide a fundamental basis for characterizations of 𝐽-self-adjoint extensions for linear nonsymmetric expressions on general time scales in terms of boundary conditions, including both differential and difference cases.