Opial properties in interpolation spaces

2021 ◽  
Author(s):  
Joanna Markowicz ◽  
Stanisław Prus
Keyword(s):  
Interpolation Spaces

scholarly journals Quasilinear evolutionary equations and continuous interpolation spaces

2004 ◽  
Vol 196 (2) ◽  
pp. 418-447 ◽  
Author(s):  
Philippe Clément ◽  
Stig-Olof Londen ◽  
Gieri Simonett
Keyword(s):  
Interpolation Spaces ◽  
Evolutionary Equations ◽  
Continuous Interpolation

scholarly journals Approximation of positive operators by analytic vectors

2020 ◽  
Vol 12 (2) ◽  
pp. 412-418
Author(s):  
M.I. Dmytryshyn
Keyword(s):  
Banach Space ◽  
Positive Operator ◽  
Invariant Subspaces ◽  
Positive Operators ◽  
Interpolation Spaces ◽  
Jackson Type ◽  
Normalization Factor ◽  
Approximation Spaces ◽  
Similar Role ◽  
Approximation Errors

We give the estimates of approximation errors while approximating of a positive operator $A$ in a Banach space by analytic vectors. Our main results are formulated in the form of Bernstein and Jackson type inequalities with explicitly calculated constants. We consider the classes of invariant subspaces ${\mathcal E}_{q,p}^{\nu,\alpha}(A)$ of analytic vectors of $A$ and the special scale of approximation spaces $\mathcal {B}_{q,p,\tau}^{s,\alpha}(A)$ associated with the complex degrees of positive operator. The approximation spaces are determined by $E$-functional, that plays a similar role as the module of smoothness. We show that the approximation spaces can be considered as interpolation spaces generated by $K$-method of real interpolation. The constants in the Bernstein and Jackson type inequalities are expressed using the normalization factor.

Eigenvalues and Entropy Moduli of Operators in Interpolation Spaces

2016 ◽  
Vol 27 (2) ◽  
pp. 1131-1177 ◽  
Author(s):  
Mieczysław Mastyło ◽  
Radosław Szwedek
Keyword(s):  
Interpolation Spaces
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