Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 5

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

On nilpotent operators

100%
Burlando L.
Studia Mathematica
|
2005
|
tom 166
|
nr 2
101-129
EN
We give several necessary and sufficient conditions in order that a bounded linear operator on a Banach space be nilpotent. We also discuss three necessary conditions for nilpotency. Furthermore, we construct an infinite family (in one-to-one correspondence with the square-summable sequences $(εₙ)_{n∈ℕ}$ of strictly positive real numbers) of nonnilpotent quasinilpotent operators on an infinite-dimensional Hilbert space, all the iterates of each of which have closed range. Each of these operators (as well as an operator previously constructed by C. Apostol in [Ap]) can be used to provide a negative answer to a question posed by M. Mbekhta and J. Zemánek [MZ]. We also use our example to show that two (equivalent to each other) of the three necessary conditions for nilpotency we have mentioned above are not sufficient, by proving that the sequence $(εₙ)_{n∈ℕ}$ can be chosen so that these two conditions are satisfied. Finally, from a generalization-obtained by using a theorem proved by M. Gonzalez and V. M. Onieva in [GO2]-of a result provided by C. Apostol in [Ap], we derive that any holomorphic function of each operator in our example, as well as of the one constructed in [Ap], has closed range.
2
Content available remote

Generalizations of Cesàro means and poles of the resolvent

100%
Burlando L.
Studia Mathematica
|
2004
|
tom 164
|
nr 3
257-281
EN
An improvement of the generalization-obtained in a previous article [Bu1] by the author-of the uniform ergodic theorem to poles of arbitrary order is derived. In order to answer two natural questions suggested by this result, two examples are also given. Namely, two bounded linear operators T and A are constructed such that $n^{-2}Tⁿ$ converges uniformly to zero, the sum of the range and the kernel of 1-T being closed, and $n^{-3} ∑_{k=0}^{n-1} A^{k}$ converges uniformly, the sum of the range of 1-A and the kernel of (1-A)² being closed. Nevertheless, 1 is a pole of the resolvent of neither T nor A.
3
Content available remote

A generalization of the uniform ergodic theorem to poles of arbitrary order

100%
Burlando L.
Studia Mathematica
|
1997
|
tom 122
|
nr 1
75-98
EN
We obtain a generalization of the uniform ergodic theorem to the sequence $(1/n^{p}) ⅀^{n-1)_{k=0} T^k$, where T is a bounded linear operator on a Banach space and p is a positive integer. Indeed, we show that uniform convergence of the sequence above, together with an additional condition which is automatically satisfied for p = 1, is equivalent to 1 being a pole of the resolvent of T plus convergence to zero of $∥T^{n}∥/n^{p}$. Furthermore, we show that the two conditions above, together, are also equivalent to 1 being a pole of order less than or equal to p of the resolvent of T, plus a certain condition ℇ(k,p), which is less restrictive than convergence to zero of $∥T^{n}∥/n^{p}$ and generalizes the condition (called condition (ℇ-k)) introduced by K. B. Laursen and M. Mbekhta in their paper [LM2] (dealing with the case p=1).
4
Content available remote

Continuity of spectrum and spectral radius in Banach algebras

100%
Burlando L.
Banach Center Publications
|
1994
|
tom 30
|
nr 1
53-100
EN
This survey deals with necessary and/or sufficient conditions for continuity of the spectrum and spectral radius functions at a point of a Banach algebra.
5
Content available remote

The closure of the invertibles in a von Neumann algebra

64%
Burlando L., Harte R.
Colloquium Mathematicum
|
1996
|
tom 69
|
nr 2
157-165
EN
In this paper we consider a subset  of a Banach algebra A (containing all elements of A which have a generalized inverse) and characterize membership in the closure of the invertibles for the elements of Â. Thus our result yields a characterization of the closure of the invertible group for all those Banach algebras A which satisfy  = A. In particular, we prove that  = A when A is a von Neumann algebra. We also derive from our characterization new proofs of previously known results, namely Feldman and Kadison's characterization of the closure of the invertibles in a von Neumann algebra and a more recent characterization of the closure of the invertibles in the bounded linear operators on a Hilbert space.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.