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On Banach algebras with closed set of algebraic elementsAbstract. A necessary and sufficient conditions are given for the set of algebraic

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(1)

n d r z e j

o l t y s ia x

On Banach algebras with closed set of algebraic elements

e m m a

(2)

h e o r e m

( l )

(3)

ing idernpotent f 2 such th a t f 2 is the characteristic function of the set F 2. Proceeding by an induction wre obtain a sequence {PJ of closed- open subsets of 9 (ft(-A) such th a t

' 1 ф Л 2 ф • • • ф * n ф

+ / » + l

(4)

OO

7 1 = 1

O O

(5)

o o .

(6)

Thus we see th a t conditions (1), (2) and (3) are not satisfied.

R e f e r e n c e s

INSTITUTE OF MATHEMATICS, A. MICKIEWICZ UNIVERSITY

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