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EnglishKato's second representation theorem is generalized to solvable sesquilinear forms. These forms need not be non-negative nor symmetric. The representation considered holds for a subclass of solvable forms (called hyper-solvable), precisely for those whose domain is exactly the domain of the square root of the modulus of the associated operator. This condition always holds for closed semibounded forms, and it is also considered by several authors for symmetric sign-indefinite forms. As a consequence, a one-to-one correspondence between hyper-solvable forms and operators, which generalizes those already known, is established.
Corso R. (2018). A Kato's second type representation theorem for solvable sesquilinear forms. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 462(1), 982-998 [10.1016/j.jmaa.2017.12.058].
| Data di pubblicazione: | 2018 | |
| Titolo: | A Kato's second type representation theorem for solvable sesquilinear forms | |
| Autori: | CORSO, Rosario (Corresponding) | |
| Citazione: | Corso R. (2018). A Kato's second type representation theorem for solvable sesquilinear forms. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 462(1), 982-998 [10.1016/j.jmaa.2017.12.058]. | |
| Rivista: | ||
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jmaa.2017.12.058 | |
| Abstract: | Kato's second representation theorem is generalized to solvable sesquilinear forms. These forms need not be non-negative nor symmetric. The representation considered holds for a subclass of solvable forms (called hyper-solvable), precisely for those whose domain is exactly the domain of the square root of the modulus of the associated operator. This condition always holds for closed semibounded forms, and it is also considered by several authors for symmetric sign-indefinite forms. As a consequence, a one-to-one correspondence between hyper-solvable forms and operators, which generalizes those already known, is established. | |
| Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica | |
| Appare nelle tipologie: | 1.01 Articolo in rivista |
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