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1
Content available remote A note on the decomposition of Fredholm operators
Schmoeger C.
Demonstratio Mathematica
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2008
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Vol. 41, nr 1
151-158
EN
We generalize a result of F. Szigeti concerning the decomposition of Fredholm operators on Banach spaces.
2
Content available remote A note Gateaux differentials of hermitian elements in Banach algebras
Herzog G., Schmoeger C.
Demonstratio Mathematica
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2008
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Vol. 41, nr 4
909-913
EN
Let A be a complex unital Banach algebra with unit 1. If a is an element of A is hermitian then we show that [...] and we give a proof of an inequality due to J. Nieto.
3
Content available remote Banach algebra homomorphisms via orthogonal projections
Herzog G., Schmoeger C.
Demonstratio Mathematica
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2006
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Vol. 39, nr 1
137-148
EN
Let A be a unital complex Banach algebra with unit e, and p1,... ,pn a collection of orthogonal projections with sum e. The aim of this note is to investigate the close connections of properties of a is an element of A and of (piapj) ia an element of Mn(A), where Mn(A) denotes the matrix algebra of all n x n matrices with entries in A.
4
Content available remote Commutativity up to a factor in Banach algebras
Schmoeger C.
Demonstratio Mathematica
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2005
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Vol. 38, nr 4
895--900
EN
In this note we explore commutativity up to a factor ab = alfa ba for Hermitian or normal elements of a complex Banach algebra. Our results generalize results obtained for bounded linear operators on Hilbert spaces.
5
Content available remote On logarithms of linear operators on Hilbert spaces
Schmoeger C.
Demonstratio Mathematica
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2002
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Vol. 35, nr 2
375-384
6
Content available remote On a class of generalized Fredholm operators, VII
Schmoeger C.
Demonstratio Mathematica
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2000
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Vol. 33, nr 1
123-130
7
Content available remote On a class of generalized Fredholm operators, VI
Schmoeger C.
Demonstratio Mathematica
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1999
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Vol. 32, nr 4
811-822
EN
Let X be a complex Banach space and T a generalized Fredholm operator on X (see [3] , [4] , [5] , [6] and [7] ). In [7] we have shown that T has a Kato decomposition (Xl, X2). We say that a Kato decomposition (Xl, X2) of T is non-trivial if X2= {0}. The main result of this paper reads as follows: Let T be a generalized Fredholm operator with a non-trivial Kato decomposition. Then (i) The subspace X2 of each Kato decomposition of T is unique if and only if T has finite ascent. (ii) The subspace Xl of each Kato decomposition of T is unique if and only if T has finite descent. (iii) T has a unique Kato decomposition if and only if 0 is a pole of the resolvent (T - lambaI)-l.
8
Content available remote On a class of generalized Fredholm operators, V
Schmoeger C.
Demonstratio Mathematica
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1999
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Vol. 32, nr 3
595-604
EN
Let X be a complex Banach space and T a bounded linear operator on X. T is called a generalized Fredholm operator if T is relatively regular and if for some pseudo-inverse S of T the operator I - ST - T is Fredholm. The main result of this paper reads as follows: T is a generalized Fredholm operator if and only if T = T1 T2 , whereT1 is a Fredholm operator with jump j(Tl ) = 0 and T2 is a finite-dimensional nilpotent operator.
9
Content available remote On a class of generalized Fredholm operators, IV
Schmoeger C.
Demonstratio Mathematica
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1999
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Vol. 32, nr 3
581-594
EN
In the present paper we investigate generalized Fredholm operators (see [15], t16] and [17]) on a complex Hilbert space H. The main results of this paper read as follows.
10
Content available remote On a class of generalized Fredholm operators, III
Schmoeger C.
Demonstratio Mathematica
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1998
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Vol. 31, nr 4
723-733
EN
In [4] and [5] we have investigated the following class of bounded linear operators on an infinite-dimensional complex Banach space X: (fi)g(X) = {T zawiera się L(X) : there is some S zawiera się L(X) such that TST = T and I - ST - TS is Fredholm}. In this paper we continue these investigations. We shall prove some results concerning the ascent and the descent of an operator in (fi)g (X). Furthermore, we shall prove a spectral mapping property of the generalized Fredholm spectrum.
11
Content available remote On a class of generalized Fredholm operators, II
Schmoeger C.
Demonstratio Mathematica
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1998
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Vol. 31, nr 4
705-722
EN
For an infinite-dimensional complex Banach space X let L(X) denote the set of all bounded linear operators on X. The set g(X) of generalized Fredholm operators is defined as g(X) = {T L(X) : there is some S L(X) such that TST = T and 1 - ST - TS is Fredholm}. In [6] we have investigated this class of operators. In the present paper we continue these ivestigations.
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