The compression of a slant Hankel operator to H2
A slant Hankel operator K? with symbol ? in L?(T) (in short L?), where T is the unit circle on the complex plane, is an operator whose representing matrix M = (aij) is given by ai,j = (?,z-2i-j), where (?, ?) is the usual inner product in L2(T) (in short L2). The operator L? denotes the compression of K? to H2(T) (in short H2). We prove that an operator L on H2 is the compression of a slant Hankel operator to H2 if and only if U *L = LU2, where U is the unilateral shift. Moreover, we show that a hyponormal L? is necessarily normal and L? can not be an isometry.
1996 ◽
Vol 144
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pp. 179-182
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1980 ◽
Vol 21
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pp. 199-204
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1969 ◽
Vol 35
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pp. 151-157
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2010 ◽
Vol 06
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pp. 1589-1607
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2001 ◽
Vol 04
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pp. 569-577
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2013 ◽
Vol 35
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pp. 1045-1055
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