A spectral theorem for bilinear compact operators in Hilbert spaces

Autor(es)

da Silva, Eduardo Brandani ; Fernandez, Dicesar L. ; de Andrade Neves, Marcus Vinicius

• Tipo de documento: Artigo Científico
• Fonte: BANACH JOURNAL OF MATHEMATICAL ANALYSIS; v. 15, n. 2, p. 36-pg., 2021-04-01.

Resumo

Current work defines Schur representation of a bilinear operator T: H x H -> H, where H is a separable Hilbert space. Introducing the concepts of self-adjoint bilinear operators, ordered eigenvalues and eigenvectors, we prove that if T is compact, self-adjoint, and its eigenvalues are ordered, then T has a Schur representation, thus obtaining a spectral theorem for T on real Hilbert spaces. We prove that the hypothesis of the existence of ordered eigenvalues is fundamental. (AU)

• Processo FAPESP: 18/19764-4 - s-Números, Interpolação e Ideais de Operadores Bilineares
• Beneficiário: Dicesar Lass Fernandez
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Brasil