## A function algebra without any point derivation.(English)Zbl 0628.46055

The authors construct a commutative Banach algebra A with unit such that $$\| f^ 2\| =\| f\|^ 2$$ holds for any $$f\in A$$ and with the following two properties:
(1) A admits no non-zero derivation at any point of the maximal ideal space M(A) of A.
(2) The Shilov boundary of A is a proper subset of M(A).
This answers a question posed by J. Wermer [J. Funct. Anal. 1, 28- 36 (1967; Zbl 0159.421)].
Reviewer: M.von Renteln

### MSC:

 46J10 Banach algebras of continuous functions, function algebras 46J20 Ideals, maximal ideals, boundaries 47B47 Commutators, derivations, elementary operators, etc.

Zbl 0159.421
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