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The limit of a
sequence of squares in an algebra need not be a square
Richard Arens |
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Vol. 137 (1989), No. 1, 15–18
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Abstract |
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Let A1 ← A2 ← A3 ←⋯ be an inverse system of Banach-algebra homomorphisms, and let f be an element of the limit algebra A. Suppose f is the limit of squares, that is, f1↤f2↤f3↤⋯↤f, where each fn has a square root in its algebra An. Does this require that f have a square root in A? Our object is to show that the answer to this as well as some similarly natural questions is ‘no’. |
Mathematical Subject Classification 2000
Primary: 46H05
Secondary: 46M40
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Milestones
Received: 2 March 1988
Published: 1 March 1989
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Authors |
| Richard Arens | |
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