Symmetric kernels of Banach ideal spaces

1985 ◽  
Vol 25 (4) ◽  
pp. 531-533 ◽  
Author(s):  
V. A. Biktasheva
Keyword(s):  
Banach Ideal Spaces

scholarly journals The Kreps-Yan theorem for Banach ideal spaces

2009 ◽  
Vol 50 (1) ◽  
pp. 162-166 ◽  
Author(s):  
D. B. Rokhlin
Keyword(s):  
Banach Ideal Spaces

Convexity and concavity of Banach ideal spaces and imbedding theorems

1991 ◽  
Vol 31 (3) ◽  
pp. 373-379
Author(s):  
M. Z. Berkolaiko
Keyword(s):  
Banach Ideal Spaces ◽  
Convexity And Concavity

scholarly journals Linear Operators and Equations with Partial Integrals

2019 ◽  
Vol 65 (3) ◽  
pp. 390-433
Author(s):  
A S Kalitvin ◽  
V A Kalitvin
Keyword(s):  
Spectral Radius ◽  
Spectral Properties ◽  
Volterra Operator ◽  
Linear Equations ◽  
Continuous Functions ◽  
Linear Operators ◽  
Fredholm Alternative ◽  
Fredholm Equations ◽  
Spaces Of Continuous Functions ◽  
Banach Ideal Spaces

We consider linear operators and equations with partial integrals in Banach ideal spaces, spaces of vector functions, and spaces of continuous functions. We study the action, regularity, duality, algebras, Fredholm properties, invertibility, and spectral properties of such operators. We describe principal properties of linear equations with partial integrals. We show that such equations are essentially different compared to usual integral equations. We obtain conditions for the Fredholm alternative, conditions for zero spectral radius of the Volterra operator with partial integrals, and construct resolvents of invertible equations. We discuss Volterra-Fredholm equations with partial integrals and consider problems leading to linear equations with partial integrals.

scholarly journals Representation of Banach Ideal Spaces and Factorization of Operators

2005 ◽  
Vol 57 (5) ◽  
pp. 897-940 ◽  
Author(s):  
Evgenii I. Berezhnoĭ ◽  
Lech Maligranda
Keyword(s):  
Orlicz Spaces ◽  
Integral Operators ◽  
Representation Theorems ◽  
Fatou Property ◽  
Schur Test ◽  
Banach Ideal Spaces

AbstractRepresentation theorems are proved for Banach ideal spaces with the Fatou property which are built by the Calderón–Lozanovskiĭ construction. Factorization theorems for operators in spaces more general than the Lebesgue Lpspaces are investigated. It is natural to extend the Gagliardo theorem on the Schur test and the Rubio de Francia theorem on factorization of the Muckenhoupt Ap weights to reflexive Orlicz spaces. However, it turns out that for the scales far fromLp-spaces this is impossible. For the concrete integral operators it is shown that factorization theorems and the Schur test in some reflexive Orlicz spaces are not valid. Representation theorems for the Calderón–Lozanovskiĭ construction are involved in the proofs.

scholarly journals Prediction Operators in Banach Ideal Spaces

2002 ◽  
Vol 114 (2) ◽  
pp. 147-151
Author(s):  
Tingfu Wang ◽  
Zheng Liu
Keyword(s):  
Banach Ideal Spaces
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