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Local spectral theory of endomorphisms of the disk algebra

Trivedi S., Chandra H.

Demonstratio Mathematica

2016

Vol. 49, nr 1

95--106

Let A(D) denote the disk algebra. Every endomorphism of A(D) is induced by some φ (…) A(D) with ║φ║ ≤ 1. In this paper, it is shown that if φ is not an automorphism of D and φ has a fixed point in the open unit disk then the endomorphism induced by φ is decomposable if and only if the fixed set of φ is singleton. Further, we determine the local spectra of the endomorphism induced by φ in the cases when the fixed set of φ either includes unit circle or is a singleton.

Retracts of Algebras

Novotny M.

Fundamenta Informaticae

2007

Vol. 75, nr 1-4

375-384

Construction of retracts of a general algebra is described by using retracts of mono-unary algebras. Inspirational influence of the theory of Pawlak machines is mentioned.

An application of Kwapień's theorem to the investigation of the structure of Lo-space

Mehemmed A. A.

Demonstratio Mathematica

2002

Vol. 35, nr 3

593-598

Our aim in this paper is to use Kwapien's theorem to show that the space LQ is prime. This was a longstanding open question posed by Pelczynski which was resolved by Kalton [3]. The proof given here uses some new lemmas which can be of interest.

Some remarks on endomorphisms of universal n-algebras

Płonka E.

Demonstratio Mathematica

2000

Vol. 33, nr 1

29-34

Endomorphism semigroups of nearrings of continuous realvalued functions

Magill K.

Demonstratio Mathematica

1998

Vol. 31, nr 1

223-234