On scalar extensions and spectral decompositions of complex symmetric operators

• Published in: Journal of mathematical analysis and applications Vol. 384; no. 2; pp. 252 - 260
• Main Authors: Jung, Sungeun, Ko, Eungil, Lee, Ji Eun
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 15.12.2011; Elsevier
• Subjects: Complex symmetric operator; Decomposable; Exact sciences and technology; Mathematical analysis; Mathematics; Operator theory; Property ( δ); Sciences and techniques of general use; Spectral decompositions; Subscalar; Complex symmetric operator; Property ( δ); Spectral decompositions; Decomposable; Subscalar; Spectral operator; Invariant subspace; Mathematical analysis; Spectral properties; Property (δ)

In this paper we prove that a complex symmetric operator with property ( δ) is subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. We also provide various relations for spectral decomposition properties between complex symmetric operators and...