Closed operator ideals and limiting real interpolation

2014 ◽  
Vol 220 (2) ◽  
pp. 187-196 ◽  
Author(s):  
Luz M. Fernández-Cabrera ◽  
Antón Martínez
Keyword(s):  
Closed Operator ◽  
Real Interpolation ◽  
Operator Ideals

Duality of the distance to closed operator ideals

2003 ◽  
Vol 133 (1) ◽  
pp. 197-212 ◽  
Author(s):  
Hans-Olav Tylli
Keyword(s):  
Banach Spaces ◽  
Closed Operator ◽  
Operator Ideal ◽  
Linear Operators ◽  
Distance Functions ◽  
Approximation Properties ◽  
Operator Ideals ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Special Operator

Special operator-ideal approximation properties (APs) of Banach spaces are employed to solve the problem of whether the distance functions S ↦ dist(S*, I(F*, E*)) and S ↦ dist(S, I*(E, F)) are uniformly comparable in each space L(E, F) of bounded linear operators. Here, I*(E, F) = {S ∈ L(E, F) : S* ∈ I(F*, E*)} stands for the adjoint ideal of the closed operator ideal I for Banach spaces E and F. Counterexamples are obtained for many classical surjective or injective Banach operator ideals I by solving two resulting ‘asymmetry’ problems for these operator-ideal APs.

scholarly journals Extrapolation properties of closed operator ideals

2013 ◽  
Vol 38 ◽  
pp. 341-350 ◽  
Author(s):  
Luz M. Fernández-Cabrera ◽  
Antón Martínez
Keyword(s):  
Closed Operator ◽  
Operator Ideals

scholarly journals Norm closed operator ideals in Lorentz sequence spaces

2012 ◽  
Vol 389 (1) ◽  
pp. 247-260 ◽  
Author(s):  
Anna Kamińska ◽  
Alexey I. Popov ◽  
Eugeniu Spinu ◽  
Adi Tcaciuc ◽  
Vladimir G. Troitsky
Keyword(s):  
Closed Operator ◽  
Sequence Spaces ◽  
Operator Ideals

scholarly journals INTERPOLATION METHODS DEFINED BY MEANS OF POLYGONS AND COMPACT OPERATORS

2007 ◽  
Vol 50 (3) ◽  
pp. 653-671 ◽  
Author(s):  
Luz M. Fernández-Cabrera ◽  
Antón Martínez
Keyword(s):  
Banach Spaces ◽  
Necessary Conditions ◽  
Closed Operator ◽  
Compact Operators ◽  
Operator Ideals ◽  
Interpolation Methods

AbstractWe work with interpolation methods for $N$-tuples of Banach spaces associated with polygons. We compare necessary conditions for interpolating closed operator ideals with conditions required to interpolate compactness. We also establish a formula for the measure of non-compactness of interpolated operators.

Some interpolation results that are the exclusive property of compact operators

2002 ◽  
Vol 132 (2) ◽  
pp. 317-328
Author(s):  
Fernando Cobos ◽  
Luz M. Fernández-Cabrera ◽  
Antón Martínez ◽  
Evgeniy Pustylnik
Keyword(s):  
Closed Operator ◽  
Compact Operators ◽  
Operator Ideals ◽  
Interpolation Theory ◽  
Exclusive Property

We show that certain interpolation results for compact operators established by Cobos and co-workers cannot be extended to general closed operator ideals. We shall also characterize compactness of an embedding in terms of functions related to the classical K- and J-functionals of interpolation theory.

scholarly journals BEST POSSIBLE COMPACTNESS RESULTS OF LIONS–PEETRE TYPE

2001 ◽  
Vol 44 (1) ◽  
pp. 153-173 ◽  
Author(s):  
Fernando Cobos ◽  
Michael Cwikel ◽  
Pedro Matos
Keyword(s):  
Closed Operator ◽  
Subject Classification ◽  
Operator Ideals ◽  
Primary 46B70 ◽  
Dual Case

AbstractIf $T:A_{0}\rightarrow B$ boundedly and $T:A_{1}\rightarrow B$ compactly, then a result of Lions–Peetre shows that $T:A\rightarrow B$ compactly for a certain class of spaces $A$ which are intermediate with respect to $A_{0}$ and $A_{1}$. We investigate to what extent such results can hold for arbitrary intermediate spaces $A$. The ‘dual’ case of an operator $S$ such that $S:X\rightarrow Y_{0}$ boundedly and $S:X\rightarrow Y_{1}$ compactly, is also considered, as well as similar questions for other closed operator ideals.AMS 2000 Mathematics subject classification: Primary 46B70; 47D50

scholarly journals Closed operator ideals and interpolation

1980 ◽  
Vol 35 (3) ◽  
pp. 397-411 ◽  
Author(s):  
Stefan Heinrich
Keyword(s):  
Closed Operator ◽  
Operator Ideals
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