The abstract Hardy algebra situation

1977 ◽  
pp. 59-80
Author(s):  
Klaus Barbey ◽  
Heinz König
Keyword(s):  
Hardy Algebra

scholarly journals On some basic relations in the abstract Hardy algebra theory

1983 ◽  
Vol 77 (1) ◽  
pp. 29-57
Author(s):  
Heinz König
Keyword(s):  
Hardy Algebra ◽  
Algebra Theory

Elements of abstract Hardy algebra theory

1977 ◽  
pp. 81-107
Author(s):  
Klaus Barbey ◽  
Heinz König
Keyword(s):  
Hardy Algebra ◽  
Algebra Theory

scholarly journals Coherence of the real symmetric Hardy algebra

2011 ◽  
pp. 303-308
Author(s):  
Tirthankar Bhattacharyya ◽  
Amol Sasane
Keyword(s):  
The Real ◽  
Hardy Algebra

An invariant subspace theorem in the abstract Hardy algebra theory

1982 ◽  
Vol 39 (1) ◽  
pp. 51-58 ◽  
Author(s):  
Reiner Kallenborn ◽  
Heinz König
Keyword(s):  
Invariant Subspace ◽  
Subspace Theorem ◽  
Hardy Algebra ◽  
Algebra Theory

scholarly journals Andô dilations and inequalities on non-commutative domains

2018 ◽  
Vol 148 (6) ◽  
pp. 1239-1267
Author(s):  
Gelu Popescu
Keyword(s):  
Type Representation ◽  
Hardy Algebras ◽  
Commuting Operators ◽  
Commutant Lifting ◽  
Hardy Algebra ◽  
The Matrix ◽  
Commutant Lifting Theorem ◽  
Weak Operator ◽  
Commuting Contractions ◽  
Matrix Case

We obtain intertwining dilation theorems for non-commutative regular domains 𝒟f and non-commutative varieties 𝒱J in B(𝓗)n, which generalize Sarason and Szőkefalvi-Nagy and Foiaş's commutant lifting theorem for commuting contractions. We present several applications including a new proof for the commutant lifting theorem for pure elements in the domain 𝒟f (respectively, variety 𝒱J ) as well as a Schur-type representation for the unit ball of the Hardy algebra associated with the variety 𝒱J. We provide Andô-type dilations and inequalities for bi-domains 𝒟f ×c 𝒟g consisting of all pairs (X,Y ) of tuples X := (X1,…, Xn1) ∊ 𝒟f and Y := (Y1,…, Yn2) ∊ 𝒟g that commute, i.e. each entry of X commutes with each entry of Y . The results are new, even when n1 = n2 = 1. In this particular case, we obtain extensions of Andô's results and Agler and McCarthy's inequality for commuting contractions to larger classes of commuting operators. All the results are extended to bi-varieties 𝒱J1×c 𝒱J2, where 𝒱J1 and 𝒱J2 are non-commutative varieties generated by weak-operator-topology-closed two-sided ideals in non-commutative Hardy algebras. The commutative case and the matrix case when n1 = n2 = 1 are also discussed.

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