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1
Content available remote

On the joint spectral radius

100%
Müller V.
Annales Polonici Mathematici
|
1997
|
tom 66
|
nr 1
173-182
EN
We prove the $𝓁_p$-spectral radius formula for n-tuples of commuting Banach algebra elements
2
Content available remote

Local behaviour of operators

100%
Müller V.
Banach Center Publications
|
1994
|
tom 30
|
nr 1
251-258
3
Content available remote

Nil, nilpotent and PI-algebras

100%
Müller V.
Banach Center Publications
|
1994
|
tom 30
|
nr 1
259-265
EN
The notions of nil, nilpotent or PI-rings (= rings satisfying a polynomial identity) play an important role in ring theory (see e.g. [8], [11], [20]). Banach algebras with these properties have been studied considerably less and the existing results are scattered in the literature. The only exception is the work of Krupnik [13], where the Gelfand theory of Banach PI-algebras is presented. However, even this work has not get so much attention as it deserves. The present paper is an attempt to give a survey of results concerning Banach nil, nilpotent and PI-algebras. The author would like to thank to J. Zemánek for essential completion of the bibliography.
4
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The joint essential numerical range, compact perturbations, and the Olsen problem

100%
Müller V.
Studia Mathematica
|
2010
|
tom 197
|
nr 3
275-290
EN
Let T₁,...,Tₙ be bounded linear operators on a complex Hilbert space H. Then there are compact operators K₁,...,Kₙ ∈ B(H) such that the closure of the joint numerical range of the n-tuple (T₁-K₁,...,Tₙ-Kₙ) equals the joint essential numerical range of (T₁,...,Tₙ). This generalizes the corresponding result for n = 1. We also show that if S ∈ B(H) and n ∈ ℕ then there exists a compact operator K ∈ B(H) such that $||(S-K)ⁿ|| = ||Sⁿ||_{e}$. This generalizes results of C. L. Olsen.
5
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The Słodkowski spectra and higher Shilov boundaries

100%
Müller V.
Studia Mathematica
|
1993
|
tom 105
|
nr 1
69-75
EN
We investigate relations between the spectra defined by Słodkowski [14] and higher Shilov boundaries of the Taylor spectrum. The results generalize the well-known relation between the approximate point spectrum and the usual Shilov boundary.
6
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Axiomatic theory of spectrum III: semiregularities

100%
Müller V.
Studia Mathematica
|
2000
|
tom 142
|
nr 2
159-169
EN
We introduce and study the notions of upper and lower semiregularities in Banach algebras. These notions generalize the previously studied notion of regularity - a class is a regularity if and only if it is both upper and lower semiregularity. Each semiregularity defines in a natural way a spectrum which satisfies a one-way spectral mapping property (the spectrum defined by a regularity satisfies the both-ways spectral mapping property).
7
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Local spectrum and local spectral radius of an operator at a fixed vector

64%
Bračič J., Müller V.
Studia Mathematica
|
2009
|
tom 194
|
nr 2
155-162
EN
Let 𝒳 be a complex Banach space and e ∈ 𝒳 a nonzero vector. Then the set of all operators T ∈ ℒ(𝒳) with $σ_{T}(e) = σ_δ(T)$, respectively $r_{T}(e) = r(T)$, is residual. This is an analogy to the well known result for a fixed operator and variable vector. The results are then used to characterize linear mappings preserving the local spectrum (or local spectral radius) at a fixed vector e.
8
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A product of three projections

64%
Kopecká E., Müller V.
Studia Mathematica
|
2014
|
tom 223
|
nr 2
175-186
EN
Let X and Y be two closed subspaces of a Hilbert space. If we send a point back and forth between them by orthogonal projections, the iterates converge to the projection of the point onto the intersection of X and Y by a theorem of von Neumann. Any sequence of orthoprojections of a point in a Hilbert space onto a finite family of closed subspaces converges weakly, according to Amemiya and Ando. The problem of norm convergence was open for a long time. Recently Adam Paszkiewicz constructed five subspaces of an infinite-dimensional Hilbert space and a sequence of projections on them which does not converge in norm. We construct three such subspaces, resolving the problem fully. As a corollary we observe that the Lipschitz constant of a certain Whitney-type extension does in general depend on the dimension of the underlying space.
9
Content available remote

Hypercyclic sequences of operators

64%
León-Saavedra F., Müller V.
Studia Mathematica
|
2006
|
tom 175
|
nr 1
1-18
EN
A sequence (Tₙ) of bounded linear operators between Banach spaces X,Y is said to be hypercyclic if there exists a vector x ∈ X such that the orbit Tₙx is dense in Y. The paper gives a survey of various conditions that imply the hypercyclicity of (Tₙ) and studies relations among them. The particular case of X = Y and mutually commuting operators Tₙ is analyzed. This includes the most interesting cases (Tⁿ) and (λₙTⁿ) where T is a fixed operator and λₙ are complex numbers. We also study when a sequence of operators has a large (either dense or closed infinite-dimensional) manifold consisting of hypercyclic vectors.
10
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Spectral radius formula for commuting Hilbert space operators

64%
Müller V., Sołtysiak A.
Studia Mathematica
|
1992
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tom 103
|
nr 3
329-333
EN
A formula is given for the (joint) spectral radius of an n-tuple of mutually commuting Hilbert space operators analogous to that for one operator. This gives a positive answer to a conjecture raised by J. W. Bunce in [1].
11
Content available remote

On spectral properties of linear combinations of idempotents

52%
Du H.-K., Deng C.-Y., Mbekhta M., Müller V.
Studia Mathematica
|
2007
|
tom 180
|
nr 3
211-217
EN
Let P,Q be two linear idempotents on a Banach space. We show that the closedness of the range and complementarity of the kernel (range) of linear combinations of P and Q are independent of the choice of coefficients. This generalizes known results and shows that many spectral properties of linear combinations do not depend on their coefficients.
12
Content available remote

On the semi-Browder spectrum

52%
Kordula V., Müller V., Rakočević V.
Studia Mathematica
|
1997
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tom 123
|
nr 1
1-13
EN
An operator in a Banach space is called upper (lower) semi-Browder if it is upper (lower) semi-Fredholm and has a finite ascent (descent). We extend this notion to n-tuples of commuting operators and show that this notion defines a joint spectrum. Further we study relations between semi-Browder and (essentially) semiregular operators.
13
Content available remote

Adjoining inverses to noncommutative Banach algebras and extensions of operators

50%
Müller V.
Studia Mathematica
|
1988
|
tom 91
|
nr 1
73-77
14
Content available remote

Spectrum of generators of a noncommutative Banach algebra

45%
Müller V., Sołtysiak A.
Studia Mathematica
|
1989
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tom 93
|
nr 1
87-95
15
Content available remote

Renormalizations of Banach and locally convex algebras

45%
Fernández A., Müller V.
Studia Mathematica
|
1990
|
tom 96
|
nr 3
237-242
16
Content available remote

Inverse elements in extensions of Banach algebras

38%
Müller V.
Studia Mathematica
|
1984
|
tom 80
|
nr 2
191-195
17
Content available remote

Removability of ideals in commutative Banach algebras

38%
Müller V.
Studia Mathematica
|
1984
|
tom 78
|
nr 3
297-307
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