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- W1998207908 abstract "Kaplansky density theorem is extremely useful in dealing with *-algebras of operators. This theorem says that if A is a C*-algebra of B ( H ) with a strong closure M , then the unit ball A 1 of A is strongly dense in the unit ball M 1 of M . Many deep results for the operator algebra are deduced with this technical tool. The main purpose of this paper is to give a relevant density result in Pontrjagin space. Suppose that A is an operator algebra in Pontrjagin space. Denote A 1 = {A ∣ A ∈ A , σ(A*A) ⊂ (|z| ≤ 1)}. For any set of operators A , denote the strong closure of A by [formula] s . We prove the following theorem. Theorem. Let A be a norm closed self-adjoint algebra of operators in Pontrjagin space, M = [formula] s . Then ([formula] 1 ) s ⊃ M 1 ." @default.
- W1998207908 created "2016-06-24" @default.
- W1998207908 creator A5068927615 @default.
- W1998207908 date "2002-04-01" @default.
- W1998207908 modified "2023-09-27" @default.
- W1998207908 title "A Density Theorem on the Operator Algebra in Pontrjagin Space" @default.
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- W1998207908 doi "https://doi.org/10.1006/jmaa.2001.7804" @default.
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