Fixed points of commutative Lüders operations

Fixed Points of Quantum Operations

Quantum operations frequently occur in quantum measurement theory, quantum probability, quantum computation and quantum information theory. If an operator A is invariant under a quantum operation φ we call A a φ-fixed point. Physically, the φ-fixed points are the operators that are not disturbed by the action of φ. Our main purpose is to answer the following question. If A is a φ-fixed point, i...

Fixed Points of Elementary Commutative Groups

In this Note G is always a compact Lie group. A G-space is a topological space on which G acts continuously. We shall be mainly concerned with the case where G is an elementary commutative p-group {p prime or zero), that is, a direct product of a finite number of copies of the circle group T if p = 0 or of the cyclic group Zp of order p if p is prime. In this study, a basic role is played by th...

Common Fixed Points of Commutative Semigroups of Nonexpansive Mappings

Let C be a closed convex subset of a Banach space E. A mapping T on C is called a nonexpansive mapping if ‖Tx− Ty‖ ≤ ‖x− y‖ for all x, y ∈ C. We denote by F (T ) the set of fixed points of T . Kirk [21] proved that F (T ) is nonempty in the case that C is weakly compact and has normal structure. See also [3, 4, 5, 14] and others. If C is weakly compact and E has the Opial property, then C has n...

Approximating fixed points of generalized nonexpansive mappings

Diagonal arguments and fixed points

‎A universal schema for diagonalization was popularized by N.S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fi...