TY - JOUR
T1 - THE HARDY–WEYL ALGEBRA
AU - Agler, Jim
AU - McCarthy, John E.
N1 - Publisher Copyright:
© Copyright by THETA, 2024
PY - 2024
Y1 - 2024
N2 - We study the algebra A generated by the Hardy operator H and the operator Mx of multiplication by x on L2[0, 1]. We call A the Hardy–Weyl algebra. We show that its quotient by the compact operators is isomorphic to the algebra of functions that are continuous on Λ and analytic on the interior of Λ for a planar set Λ = [−1, 0] ∪ D(1, 1), which we call the lollipop. We find a Toeplitz-like short exact sequence for the C∗-algebra generated by A. We study the operator Z = H − Mx, show that its point spectrum is (−1, 0] ∪D(1, 1), and that the eigenvalues grow in multiplicity as the points move to 0 from the left.
AB - We study the algebra A generated by the Hardy operator H and the operator Mx of multiplication by x on L2[0, 1]. We call A the Hardy–Weyl algebra. We show that its quotient by the compact operators is isomorphic to the algebra of functions that are continuous on Λ and analytic on the interior of Λ for a planar set Λ = [−1, 0] ∪ D(1, 1), which we call the lollipop. We find a Toeplitz-like short exact sequence for the C∗-algebra generated by A. We study the operator Z = H − Mx, show that its point spectrum is (−1, 0] ∪D(1, 1), and that the eigenvalues grow in multiplicity as the points move to 0 from the left.
KW - Hardy operator
KW - Hardy–Weyl algebra
KW - lollipop algebra
UR - http://www.scopus.com/inward/record.url?scp=85196022322&partnerID=8YFLogxK
U2 - 10.7900/jot.2022jun15.2387
DO - 10.7900/jot.2022jun15.2387
M3 - Article
AN - SCOPUS:85196022322
SN - 0379-4024
VL - 91
SP - 521
EP - 544
JO - Journal of Operator Theory
JF - Journal of Operator Theory
IS - 2
ER -