On Infinite Matrices, Schur Products and Operator Measures

Jukka Kiukas*, Pekka Lahti, Juha Pekka Pellonp

*Awdur cyfatebol y gwaith hwn

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid

Crynodeb

Measures with values in the set of sesquilinear forms on a subspace of a Hilbert space are of interest in quantum mechanics, since they can be interpreted as observables with only a restricted set of possible measurement preparations. In this paper, we consider the question under which conditions such a measure extends to an operator-valued measure, in the concrete setting where the measure is defned on the Borel sets of the interval [0, 2π) and is covariant with respect to shifts, in this case, the measure is characterized with a single infinite matrix, and it turns out that a basic sufficient condition for the extensibility is that the matrix be a Schur multiplier. Accordingly, we also study the connection between the extensibility problem and the theory of Schur multipliers. In particular, we define some new norms for Schur multipliers.

Iaith wreiddiolSaesneg
Tudalennau (o-i)375-393
Nifer y tudalennau19
CyfnodolynReports on Mathematical Physics
Cyfrol58
Rhif cyhoeddi3
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - 01 Rhag 2006
Cyhoeddwyd yn allanolIe

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