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Journal of Operator Theory

Volume 68, Issue 1, Summer 2012  pp. 241-256.

The Glazman-Krein-Naimark theory for Hermitian subspaces

Authors:  Yuming Shi
Author institution: Department of Mathematics, Shandong University, Jinan, Shandong 250100, P.R. China

Summary:  In this paper, self-adjoint extensions for Hermitian subspaces are studied. By applying the results about self-adjoint extensions for Hermitian subspaces obtained by E.A. Coddington in 1973, the Glazman--Krein--Naimark theory for densely defined Hermitian operators is extended to Hermitian subspaces. This result will provide a fundamental basis for characterizations of self-adjoint extensions for linear Hamiltonian systems on general time scales in terms of boundary conditions, including both continuous and discrete cases with or without certain definiteness conditions.

Keywords:  Self-adjoint extension, Hermitian subspace, GKN-set

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