Naslov
Quadratic functionals on modules over complex Banach-algebras with an approximate identity

Autori
Ilišević, Dijana

Izvornik
Studia mathematica (0039-3223) 171 (2005), 2; 103-123

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Banach-algebra ; approximate identity ; C-algebra ; H-algebra ; trace class ; standard operator algebra ; right module ; pre-Hilbert module ; normed module ; quadratic functional ; sesquilinear form ; Jordan-derivation ; double centralizer

Sažetak
The problem of the representability of quadratic functionals by sesquilinear forms is studied in this article in the setting of a module over an algebra that belongs to a certain class of complex Banach-algebras with an approximate identity. That class includes C-aalgebras as well as H-algebras and their trace classes. Each quadratic functional acting on such a module can be represented by a unique sesquilinear form. That form generally takes values in a larger algebra than the given quadratic functional does. In some special cases, such as when the module is also a complex vector space compatible with the vector space of the underlying algebra, and when the quadratic functional is positive definite with values in a C*-algebra or in the trace class for an H*-algebra, the resulting sesquilinear form takes values in the same algebra. In particular, every normed module over a C-algebra, or an H-algebra, without nonzero commutative closed two-sided ideals is a pre-Hilbert module. Furthermore, the representation theorem for quadratic functionals acting on modules over standard operator algebras is also obtained.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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