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Common fixed points of Greguš type multi-valued mappings

R. A. Rashwan, Magdy A. Ahmed (2002)

Archivum Mathematicum

This work is considered as a continuation of [19,20,24]. The concepts of δ -compatibility and sub-compatibility of Li-Shan [19, 20] between a set-valued mapping and a single-valued mapping are used to establish some common fixed point theorems of Greguš type under a φ -type contraction on convex metric spaces. Extensions of known results, especially theorems by Fisher and Sessa [11] (Theorem B below) and Jungck [16] are thereby obtained. An example is given to support our extension.

Commutants and derivation ranges

Salah Mecheri (1999)

Czechoslovak Mathematical Journal

In this paper we obtain some results concerning the set = R ( δ A ) ¯ { A } ' A ( H ) , where R ( δ A ) ¯ is the closure in the norm topology of the range of the inner derivation δ A defined by δ A ( X ) = A X - X A . Here stands for a Hilbert space and we prove that every compact operator in R ( δ A ) ¯ w { A * } ' is quasinilpotent if A is dominant, where R ( δ A ) ¯ w is the closure of the range of δ A in the weak topology.

Commutants of certain multiplication operators on Hilbert spaces of analytic functions

K. Seddighi, S. Vaezpour (1999)

Studia Mathematica

This paper characterizes the commutant of certain multiplication operators on Hilbert spaces of analytic functions. Let A = M z be the operator of multiplication by z on the underlying Hilbert space. We give sufficient conditions for an operator essentially commuting with A and commuting with A n for some n>1 to be the operator of multiplication by an analytic symbol. This extends a result of Shields and Wallen.

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