Generalized slant Toeplitz operators on H2

✍ Scribed by S. C. Arora; Ruchika Batra

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 154 KB
• Volume: 278
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310244

✦ Synopsis

For an integer k ≥ 2, k th -order slant Toeplitz operator Uϕ [1] with symbol ϕ in L ∞ (T), where T is the unit circle in the complex plane, is an operator whose representing matrix M = (αij ) is given by αij = ϕ, z ki-j , where . , . is the usual inner product in L 2 (T). The operator Vϕ denotes the compression of Uϕ to H 2 (T) (Hardy space). Algebraic and spectral properties of the operator Vϕ are discussed. It is proved that spectral radius of Vϕ equals the spectral radius of Uϕ, if ϕ is analytic or co-analytic, and if Tϕ is invertible then the spectrum of Vϕ contains a closed disc and the interior of the disc consists of eigenvalues of infinite multiplicities.