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Operational quantities characterizing semi-Fredholm operators

100%
González M., Martinón A.
Studia Mathematica
|
1995
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tom 114
|
nr 1
13-27
EN
Several operational quantities have appeared in the literature characterizing upper semi-Fredholm operators. Here we show that these quantities can be divided into three classes, in such a way that two of them are equivalent if they belong to the same class, and are comparable and not equivalent if they belong to different classes. Moreover, we give a similar classification for operational quantities characterizing lower semi-Fredholm operators.
2
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On incomparability of Banach spaces

100%
González M., Martinón A.
Banach Center Publications
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1994
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tom 30
|
nr 1
161-174
EN
Several concepts of incomparability of Banach spaces have been considered in the literature, which allow one to describe some of the properties of the product of two Banach spaces as a juxtaposition of the corresponding properties of the factors. In this paper we study the relations between these concepts of incomparability, survey the main results and applications, and state some open problems.
3
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Powers of m-isometries

81%
Bermúdez T., Díaz Mendoza C., Martinón A.
Studia Mathematica
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2012
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tom 208
|
nr 3
249-255
EN
A bounded linear operator T on a Banach space X is called an (m,p)-isometry for a positive integer m and a real number p ≥ 1 if, for any vector x ∈ X, $∑_{k=0}^{m} (-1)^{k} ({m \atop k}) ||T^{k}x||^{p} = 0$. We prove that any power of an (m,p)-isometry is also an (m,p)-isometry. In general the converse is not true. However, we prove that if $T^{r}$ and $T^{r+1}$ are (m,p)-isometries for a positive integer r, then T is an (m,p)-isometry. More precisely, if $T^{r}$ is an (m,p)-isometry and $T^{s}$ is an (l,p)-isometry, then $T^{t}$ is an (h,p)-isometry, where t = gcd(r,s) and h = min(m,l).
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