Extensions of a theorem of Fuglede and Putnam
نویسندگان
چکیده
منابع مشابه
On 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 کاملNote 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 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 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.
متن کاملFUGLEDE-PUTNAM THEOREM FOR w-HYPONORMAL OR CLASS Y OPERATORS
An asymmetric Fuglede-Putnam’s Theorem for w−hyponormal operators and class Y operators is proved, as a consequence of this result, we obtain that the range of the generalized derivation induced by the above classes of operators is orthogonal to its kernel.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1978
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1978-0487554-2