Complex interpolation and regular operators between Banach lattices

1994 ◽  
Vol 62 (3) ◽  
pp. 261-269 ◽  
Author(s):  
Gilles Pisier
Keyword(s):  
Banach Lattices ◽  
Complex Interpolation ◽  
Regular Operators

Some properties of the space of regular operators on atomic Banach lattices

2010 ◽  
Vol 62 (2) ◽  
pp. 131-137 ◽  
Author(s):  
Qingying Bu ◽  
Yongjin Li ◽  
Xiaoping Xue
Keyword(s):  
Banach Lattices ◽  
Regular Operators

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.

scholarly journals (p, q)-Regular operators between Banach lattices

2018 ◽  
Vol 188 (2) ◽  
pp. 321-350
Author(s):  
Enrique A. Sánchez Pérez ◽  
Pedro Tradacete
Keyword(s):  
Banach Lattices ◽  
Regular Operators

scholarly journals Ideal properties of regular operators between Banach lattices

1985 ◽  
Vol 29 (3) ◽  
pp. 382-400 ◽  
Author(s):  
N. J. Kalton ◽  
Paulette Saab
Keyword(s):  
Banach Lattices ◽  
Regular Operators

Fractional abstract Cauchy problem on complex interpolation scales

2020 ◽  
Vol 23 (4) ◽  
pp. 1125-1140
Author(s):  
Andriy Lopushansky ◽  
Oleh Lopushansky ◽  
Anna Szpila
Keyword(s):  
Cauchy Problem ◽  
Time Derivative ◽  
Abstract Cauchy Problem ◽  
Initial Boundary ◽  
Sectorial Operator ◽  
Complex Interpolation ◽  
Bounded Domains ◽  
Initial Boundary Value Problems ◽  
Fractional Time Derivative ◽  
Initial Boundary Value

AbstractAn fractional abstract Cauchy problem generated by a sectorial operator is investigated. An inequality of coercivity type for its solution with respect to a complex interpolation scale generated by a sectorial operator with the same parameters is established. An application to differential parabolic initial-boundary value problems in bounded domains with a fractional time derivative is shown.

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