The Complex Interpolation Method Preserves Compactness of Linear Operators

2013 ◽  
Vol 41 (1) ◽  
pp. 115-120 ◽  
Author(s):  
Nuno C. Freire
Keyword(s):  
Interpolation Method ◽  
Linear Operators ◽  
Complex Interpolation

Research about Influencing Factor on Interpolation Accuracy in Data Exchange of Fluid-Structure Interaction

2013 ◽  
Vol 318 ◽  
pp. 100-107
Author(s):  
Zhen Shen ◽  
Biao Wang ◽  
Hui Yang ◽  
Yun Zheng
Keyword(s):  
Data Exchange ◽  
Shape Function ◽  
Interpolation Method ◽  
Matching Condition ◽  
Optimal Interpolation ◽  
Complex Interpolation ◽  
Interpolation Function ◽  
Interpolation Methods ◽  
Interpolation Accuracy ◽  
Lower Accuracy

Six kinds of interpolation methods, including projection-shape function method, three-dimensional linear interpolation method, optimal interpolation method, constant volume transformation method and so on, were adoped in the study of interpolation accuracy. From the point of view about the characterization of matching condition of two different grids and interpolation function, the infuencing factor on the interpolation accuracy was studied. The results revealed that different interpolation methods had different interpolation accuracy. The projection-shape function interpolation method had the best effect and the more complex interpolation function had lower accuracy. In many cases, the matching condition of two grids had much greater impact on the interpolation accuracy than the method itself. The error of interpolation method is inevitable, but the error caused by the grid quality could be reduced through efforts.

scholarly journals ON THE STABILITY OF THE DIFFERENTIAL PROCESS GENERATED BY COMPLEX INTERPOLATION

2020 ◽  
pp. 1-32
Author(s):  
Jesús M. F. Castillo ◽  
Willian H. G. Corrêa ◽  
Valentin Ferenczi ◽  
Manuel González
Keyword(s):  
Unit Circle ◽  
Banach Spaces ◽  
Local Stability ◽  
Interpolation Method ◽  
Complex Interpolation ◽  
Analytic Family ◽  
Köthe Spaces ◽  
The Stability ◽  
Stability Results ◽  
Differential Process

We study the stability of the differential process of Rochberg and Weiss associated with an analytic family of Banach spaces obtained using the complex interpolation method for families. In the context of Köthe function spaces, we complete earlier results of Kalton (who showed that there is global bounded stability for pairs of Köthe spaces) by showing that there is global (bounded) stability for families of up to three Köthe spaces distributed in arcs on the unit circle while there is no (bounded) stability for families of four or more Köthe spaces. In the context of arbitrary pairs of Banach spaces, we present some local stability results and some global isometric stability results.

Interpolation of Morrey Spaces on Metric Measure Spaces

2014 ◽  
Vol 57 (3) ◽  
pp. 598-608 ◽  
Author(s):  
Yufeng Lu ◽  
Dachun Yang ◽  
Wen Yuan
Keyword(s):  
Interpolation Method ◽  
Interpolation Theorem ◽  
Morrey Spaces ◽  
Complex Interpolation ◽  
Metric Measure Spaces ◽  
Interpolation Methods ◽  
Measure Spaces

AbstractIn this article, via the classical complex interpolation method and some interpolation methods traced to Gagliardo, the authors obtain an interpolation theorem for Morrey spaces on quasimetric measure spaces, which generalizes some known results on ℝn.

scholarly journals ON ONE APPROXIMATION ESTIMATE

2017 ◽  
Vol 17 (5) ◽  
pp. 53-59
Author(s):  
M.B. Medegey
Keyword(s):  
Interpolation Method ◽  
Linear Operators ◽  
Approximation Estimate ◽  
The Given

Linear operators satisfying some conditions are considered. The given operators are a particular kind of class operators (by P.P. Korovkin). For the estimate derivation the interpolation method is used, described in the works by Yu.G. Abakumov and O.N. Shestakova

scholarly journals Stein interpolation for the real interpolation method

2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Nick Lindemulder ◽  
Emiel Lorist
Keyword(s):  
Interpolation Method ◽  
Real Interpolation ◽  
Complex Interpolation ◽  
The Real ◽  
Interpolation Methods ◽  
Complex Formulation ◽  
Closed Operators ◽  
Real Interpolation Method

AbstractWe prove a complex formulation of the real interpolation method, showing that the real and complex interpolation methods are not inherently real or complex. Using this complex formulation, we prove Stein interpolation for the real interpolation method. We apply this theorem to interpolate weighted $$L^p$$ L p -spaces and the sectoriality of closed operators with the real interpolation method.

Operators which Factor through Convex Banach Lattices

1980 ◽  
Vol 32 (6) ◽  
pp. 1482-1500 ◽  
Author(s):  
Shlomo Reisner
Keyword(s):  
Banach Spaces ◽  
Banach Lattice ◽  
Interpolation Method ◽  
Banach Lattices ◽  
Uniform Convexity ◽  
Complex Interpolation ◽  
Power Type ◽  
Convex Operator ◽  
Image Position ◽  
The Ideal

We investigate here classes of operators T between Banach spaces E and F, which have factorization of the formwhere L is a Banach lattice, V is a p-convex operator, U is a q-concave operator (definitions below) and jF is the cannonical embedding of F in F”. We show that for fixed p, q this class forms a perfect normed ideal of operators Mp, q, generalizing the ideal Ip,q of [5]. We prove (Proposition 5) that Mp, q may be characterized by factorization through p-convex and q-concave Banach lattices. We use this fact together with a variant of the complex interpolation method introduced in [1], to show that an operator which belongs to Mp, q may be factored through a Banach lattice with modulus of uniform convexity (uniform smoothness) of power type arbitrarily close to q (to p). This last result yields similar geometric properties in subspaces of spaces having G.L. – l.u.st.

Generalized duality and product of some noncommutative symmetric spaces

2016 ◽  
Vol 27 (10) ◽  
pp. 1650082 ◽  
Author(s):  
Yazhou Han
Keyword(s):  
Banach Spaces ◽  
Product Space ◽  
Symmetric Spaces ◽  
Von Neumann Algebra ◽  
Interpolation Method ◽  
Complex Interpolation ◽  
Von Neumann

Let [Formula: see text] and [Formula: see text] be two symmetric quasi-Banach spaces and let [Formula: see text] be a semifinite von Neumann algebra. The purpose of this paper is to study the product space [Formula: see text] and the space of multipliers from [Formula: see text] to [Formula: see text], i.e. [Formula: see text]. These spaces share many properties with their classical counterparts. Let [Formula: see text] It is shown that if [Formula: see text] is [Formula: see text]-convex fully symmetric and [Formula: see text] is [Formula: see text]-convex, then [Formula: see text], where [Formula: see text] and [Formula: see text] is the space of multipliers from [Formula: see text] to [Formula: see text] As an application, we give conditions on when [Formula: see text] Moreover, we show that the product space can be described with the help of complex interpolation method.

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