Locally C∗-equivalent algebras

Cuntz, Joachim

doi:10.1016/0022-1236(76)90068-9

Cited by 18 publications

(5 citation statements)

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“…When B is a complex unital Banach *-algebra, Cuntz (6) has shown that B is a C*-algebra in an equivalent norm if and only if Q{1, b) is a C*algebra in an equivalent norm for each self-adjoint b in B. However, the methods he uses do not generalize to the case of Banach Jordan algebras.…”

Section: Discussionmentioning

confidence: 99%

Equivalent norms on Banach Jordan algebras

Youngson¹

1979

Math. Proc. Camb. Phil. Soc.

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1. Introduction. Recently Kaplansky suggested the definition of a suitable Jordan analogue of B*-algebras, which we call J B*-algebras (see (10) and (11)). In this article, we give a characterization of those complex unital Banach Jordan algebras which are J B*-algebras in an equivalent norm. This is done by generalizing results of Bonsall ((3) and (4)) to give necessary and sufficient conditions on a real unital Banach Jordan algebra under which it is the self-adjoint part of a J B*-algebra in an equivalent norm. As a corollary we also obtain a characterization of the cones in a Banach Jordan algebra which are the set of positive elements of a J B*-algebra.

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Section: Discussionmentioning

confidence: 99%

Equivalent norms on Banach Jordan algebras

Youngson¹

1979

Math. Proc. Camb. Phil. Soc.

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“…Furthermore A. I. Loginov and V. S. Shulman [10] (see [15] and [16] for a more transparent presentation) proved the corresponding result for norm-closed J-symmetric algebras in Π k -spaces was obtained: a J-symmetric algebra A ⊂ B(H) has no invariant subspaces if and only if its norm-closure contains the algebra K(H). The proof is quite complicated and uses the striking theorem of J. Cuntz [4] about C * -equivalent Banach *-algebras.…”

Section: J-symmetric Algebras and Burnside-type Theoremsmentioning

confidence: 99%

Pontryagin-Krein Theorem: Lomonosov's proof and related results

Kissin¹,

Shulman²,

Turovskiı³

2020

Preprint

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“…(Almost Hermitian representations constitute probably the largest class of representations for which such similarity exists.) The most decisive step for proving Theorem 4 is the result obtained in Theorem 3: irreducible, uniformly closed J-symmetric operator algebras on Π fc -spaces contain the algebra of all compact operators.This last result was announced in [24] and its proof is based on Cuntz's theorem [6] and on some techniques developed in [41].…”

Section: The General Case When N(s)mentioning

confidence: 99%

“…By Theorem 2, all these subalgebras are C*-equivalent. Cuntz [6] proved that a Banach *-algebra is C*-equivalent if the closed commutative *-subalgebra generated by any selfadjoint element of the algebra is C*-equivalent. Applying this result to the algebra £?, we obtain that it is C*-equivalent.…”

Section: Theorem 3 An Irreducible Uniformly Closed J-symmetric Opementioning

confidence: 99%