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For two essentially bounded Lebesgue measurable functions $ \phi $ and $ \xi $ on unit circle $ \mathbb{T}$, we attempt to study properties of operators $ S_{\mathcal{M}(\phi, \xi)}^k = S_{T_\phi}^k + S_{H_\xi}^k$ on $ H^2(\mathbb{T}) $ ($ k \geq 2 $), where $ S_{T_\phi}^k $ is a $k^{th}$-order slant Toeplitz operator with symbol $\phi $ and $ S_{H_\xi}^k $ is a $k^{th}$-order slant Hankel operator with symbol $\xi $. The spectral properties of operators $ S_{\mathcal{M}(\phi, \phi)}^k $ (or simply $ S_{\mathcal{M}(\phi)}^k $) are investigated on $ H^2(\mathbb{T}) $. More precisely, it is proved that for $ k =2 $, the Coburn's type theorem holds for $ S_{\mathcal{M}(\phi)}^k $. The conditions under which operators $ S_{\mathcal{M}(\phi)}^k $ commute are also explored.
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참고문헌 (9)
참고문헌 신청
S. C. Arora / 2005 / Generalized slant Toeplitz operators on H2 / Math. Nachr 278(4):347~355
S. C. Arora / 2006 / Slant Hankel operators / Arch. Math. (Brno) 42(2):125~133
S. C. Arora / 2008 / The compression of a kth-order slant Hankel operator / Ganita 59(1):1~11
E. L. Basor / 1999 / On a class of Toeplitz + Hankel operators / New York J. Math 5:1~16
E. L. Basor / 2004 / Factorization theory for a class of Toeplitz + Hankel operators / J. Operator Theory 51(2):411~433
S. C. Arora / 2006 / Slant Hankel operators / Arch. Math. (Brno) 42(2):125~133
S. C. Arora / 2008 / The compression of a kth-order slant Hankel operator / Ganita 59(1):1~11
E. L. Basor / 1999 / On a class of Toeplitz + Hankel operators / New York J. Math 5:1~16
E. L. Basor / 2004 / Factorization theory for a class of Toeplitz + Hankel operators / J. Operator Theory 51(2):411~433
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