منابع مشابه
Note on a Theorem of Fuglede and Putnam
1. An involution in a ring A is a mapping a—^a* (a(Ei;A) such that a**=a, (a+b)*=a*+b*, (ab)* = b*a*. An element a&A is (1) normal if a*a=aa*, (2) self-adjoint if a*=a, (3) unitary if a*a=aa* = l (1= unity element of A). We say that "Fuglede's theorem holds in A" incase the relations a(E.A, a normal, b^A, ba=ab, imply ba* = a*b; briefly, A is an FT-ring. It follows from a theorem of B. Fuglede ...
متن کاملOn the Putnam-Fuglede theorem
We extend the Putnam-Fuglede theorem and the second-degree Putnam-Fuglede theorem to the nonnormal operators and to an elementary operator under perturbation by quasinilpo-tents. Some asymptotic results are also given.
متن کاملPutnam-fuglede Theorem and the Range-kernel Orthogonality of Derivations
Let (H) denote the algebra of operators on a Hilbert space H into itself. Let d= δ or , where δAB : (H)→ (H) is the generalized derivation δAB(S)=AS−SB and AB : (H) → (H) is the elementary operator AB(S) = ASB−S. Given A,B,S ∈ (H), we say that the pair (A,B) has the property PF(d(S)) if dAB(S) = 0 implies dA∗B∗(S) = 0. This paper characterizes operators A,B, and S for which the pair (A,B) has p...
متن کاملNote on a Theorem of Putnam ' Smichael
In a 1981 book, H. Putnam claimed that in a pure relational language without equality, for any model of a relation that was neither empty nor full, there was another model that satisses the same rst order sentences. Ed Keenan observed that this was false for nite models since equality is a deenable predicate in such cases. This note shows that Putnam's claim is true for innnite models, although...
متن کاملAn Asymmetric Putnam–fuglede Theorem for Unbounded Operators
The intertwining relations between cosubnormal and closed hyponormal (resp. cohyponormal and closed subnormal) operators are studied. In particular, an asymmetric Putnam–Fuglede theorem for unbounded operators is proved.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1959
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1959-0107826-9