MULTIPLICATION OPERATORS ON VECTOR-VALUED FUNCTION SPACES

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Atıf İçin Kopyala

Duru H., KITOVER A., Orhon M.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.141, sa.10, ss.3501-3513, 2013 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 141 Sayı: 10
• Basım Tarihi: 2013
• Doi Numarası: 10.1090/s0002-9939-2013-11603-5
• Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.3501-3513
• İstanbul Üniversitesi Adresli: Evet

Özet

Let E be a Banach function space on a probability measure space (Omega, Sigma, mu). Let X be a Banach space and E(X) be the associated Kothe-Bochner space. An operator on E(X) is called a multiplication operator if it is given by multiplication by a function in L-infinity (mu). In the main result of this paper, we show that an operator T on E(X) is a multiplication operator if and only if T commutes with L-infinity (mu) and leaves invariant the cyclic subspaces generated by the constant vector-valued functions in E(X). As a corollary we show that this is equivalent to T satisfying a functional equation considered by Calabuig, Rodriguez, and Sanchez-Perez.