Wyniki wyszukiwania

1

The single-point spectrum operators satisfying Ritt's resolvent condition

100%

Lyubich Y.

Studia Mathematica

|

2001

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tom 145

|

nr 2

135-142

EN

It is shown that an operator with the properties mentioned in the title does exist in the space $L_{p}(0,1)$, 1 ≤ p ≤ ∞. The maximal sector for the extended resolvent condition can be prescribed a priori jointly with the corresponding order of the exponential growth of the resolvent in the complementary sector.

2

Spectral localization, power boundedness and invariant subspaces under Ritt's type condition

100%

Lyubich Y.

Studia Mathematica

|

1999

|

tom 134

|

nr 2

153-167

XX

For a bounded linear operator T in a Banach space the Ritt resolvent condition $∥R_λ(T)∥ ≤ C/|λ - 1|$ (|λ| > 1) can be extended (changing the constant C) to any sector |arg(λ - 1)| ≤ π - δ, $arccos(C^{-1}) < δ < π/2$. This implies the power boundedness of the operator T. A key result is that the spectrum σ(T) is contained in a special convex closed domain. A generalized Ritt condition leads to a similar localization result and then to a theorem on invariant subspaces.

3

The real-analytic solutions of the Abel functional equation

64%

Belitskii G., Lyubich Y.

Studia Mathematica

|

1999

|

tom 134

|

nr 2

135-141

XX

For the Abel equation on a real-analytic manifold a dynamical criterion of solvability in real-analytic functions is proved.

4

Precompactness in the uniform ergodic theory

64%

Lyubich Y., Zemánek J.

Studia Mathematica

|

1994-1995

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tom 112

|

nr 1

89-97

EN

We characterize the Banach space operators T whose arithmetic means ${n^{-1}(I + T + ... + T^{n-1})}_{n ≥ 1}$ form a precompact set in the operator norm topology. This occurs if and only if the sequence ${n^{-1} T^n}_{n ≥ 1}$ is precompact and the point 1 is at most a simple pole of the resolvent of T. Equivalent geometric conditions are also obtained.

5

The Abel equation and total solvability of linear functional equations

64%

Belitskii G., Lyubich Y.

Studia Mathematica

|

1998

|

tom 127

|

nr 1

81-97

EN

We investigate the solvability in continuous functions of the Abel equation φ(Fx) - φ(x) = 1 where F is a given continuous mapping of a topological space X. This property depends on the dynamics generated by F. The solvability of all linear equations P(x)ψ(Fx) + Q(x)ψ(x) = γ(x) follows from solvability of the Abel equation in case F is a homeomorphism. If F is noninvertible but X is locally compact then such a total solvability is determined by the same property of the cohomological equation φ(Fx) - φ(x) = γ(x). The smooth situation can also be considered in this way.

Ograniczanie wyników

5 Studia Mathematica

5 Lyubich Y.

2 Belitskii G.

1 Zemánek J.

1 2001

2 1999

1 1998

1 1994

The single-point spectrum operators satisfying Ritt's resolvent condition

Spectral localization, power boundedness and invariant subspaces under Ritt's type condition

The real-analytic solutions of the Abel functional equation

Precompactness in the uniform ergodic theory

The Abel equation and total solvability of linear functional equations