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We study multiplication operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm. In addition, we determine the spectrum of the bounded multiplication operators and characterize the isometries. Finally, we study the multiplication operators between the weighted Banach spaces and the Lipschitz space by characterizing the bounded and the compact operators, determining estimates on the operator norm, and showing there are no isometries.
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참고문헌 (10)
참고문헌 신청
F. Colonna / 2010 / Multiplication operators on the Lipschitz space of a tree / Integral Equations Operator Theory 68 (3) : 391 ~ 411
F. Colonna / 2012 / Multiplication operators between the Lipschitz space and the space of bounded functions on a tree / Mediterr. J. Math 9 (3) : 423 ~ 438
J. Conway / 1990 / A Course in Functional Analysis / Springer-Verlag
M. Tjani / 1996 / Compact composition operators on M¨obius invariant Banach spaces / Ph.D. / Michigan State University
P. L. Duren / 1969 / Linear functions on Hp spaces with 0 < p < 1 / J. Reine Angew. Math 238 : 32 ~ 60
F. Colonna / 2012 / Multiplication operators between the Lipschitz space and the space of bounded functions on a tree / Mediterr. J. Math 9 (3) : 423 ~ 438
J. Conway / 1990 / A Course in Functional Analysis / Springer-Verlag
M. Tjani / 1996 / Compact composition operators on M¨obius invariant Banach spaces / Ph.D. / Michigan State University
P. L. Duren / 1969 / Linear functions on Hp spaces with 0 < p < 1 / J. Reine Angew. Math 238 : 32 ~ 60
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