Unified min-max and interlacing theorems for linear operators
| Autor: | Fernando C. Silva, Catarina Santa-Clara, Laura Iglésias |
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| Rok vydání: | 2011 |
| Předmět: |
Discrete mathematics
Multilinear algebra Algebra and Number Theory Compact Operators Modular Lattice Interlacing Eigenvalues Invariant Factors Goldie Dimension Operator theory Compact operator Singular value Principal ideal Infinite Goldie-Dimension Invariant (mathematics) Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| ISSN: | 1563-5139 0308-1087 |
| Popis: | There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant–Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77–103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case. |
| Databáze: | OpenAIRE |
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