A fixed-point theorem for certain operator valued maps
Authors: D. R. Brown and M. J. O’Malley
Journal: Proc. Amer. Math. Soc. 74 (1979), 254-258
MSC: Primary 47H10
MathSciNet review: 524296
Abstract: Let H be a real Hilbert space, and let denote the space of symmetric, bounded operators on H which have numerical range in [0, 1], topologized by the strong operator topology, and let L be a strongly continuous function on H into . In this paper, methods are given to locate all which are fixed points of L in the sense that .
In particular, if and if and are fixed positive rational numbers with , a decreasing sequence of elements of is recursively defined, and converges to . If , then Q is idempotent and is a fixed point of L, and if , then is a fixed point of L.
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