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Cubo (Temuco)

versión On-line ISSN 0719-0646

Cubo vol.15 no.3 Temuco  2013 


On centralizers of standard operator algebras with involution


Maja Fošner1, Benjamin Marcen1 and Nejc Širovnik2

1Faculty of Logistics, University of Maribor, Mariborska cesta 7 3000 Celje Slovenia,,

2Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160 2000 Maribor Slovenia.


The purpose of this paper is to prove the following result. Let be a complex Hilbert space, let () be the algebra of all bounded linear operators on and let () () be a standard operator algebra, which is closed under the adjoint operation. Let : () () be a linear mapping satisfying the relation 2(*) = ()* + *() for all (). In this case is of the form () = λ for all (), where λ is some fixed complex number.

Keywords and Phrases: ring, ring with involution, prime ring, semiprime ring, Banach space, Hilbert space, standard operator algebra, H*-algebra, left (right) centralizer, two-sided centralizer.


El propósito de este artículo es probar el siguiente resultado. Sea un espacio de Hilbert complejo, sea () el álgebra de todos los operadores lineales acotados sobre y sea () () la álgebra de operadores clásica, la cual es cerrada bajo la operación adjunto. Sea : ()() una aplicación lineal satisfaciendo la relación 2(*) = ()* + *() para todo (). En este caso, es de la forma () = λ para todo (), donde λ es un número complejo fijo.

2010 AMS Mathematics Subject Classication: 16N60, 46B99, 39B42.



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Received: April 2013 / Accepted: September 2013.

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