Partially Fundamentally Reducible Operators in Kreĭn Spaces

A self-adjoint operator A in a Krĕın space (K, [ · , · ]) is called partially fundamentally reducible if there exist a fundamental decomposition K = K+[+̇]K− (which does not reduce A) and densely defined symmetric operators S+ and S− in the Hilbert spaces (K+, [ · , · ]) and (K−,−[ · , · ]), respectively, such that each S+ and S− has defect numbers (1, 1) and the operator A is a self-adjoint extension of S = S+ ⊕ (−S−) in the Krĕın space (K, [ · , · ]). The operator A is interpreted as a coupling of operators S+ and −S−, relative to some boundary triples ( C,Γ 0 ,Γ 1 )