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Vietnam Journal of Mathematics 38:1 (2010) 45-54  

Hankel Operators with Vector Valued Symbols on the Hardy Space

Namita Das and Pabitra Kumar Jena

Abstract.  In this paper we have shown that the sequence {} converges strongly to the Hankel operator SΦ L(H2Cn(T))for Φ LMn(T)and for all inner functions q H(T). Here TΦ is the Toeplitz operator on the Hardy space H2Cn(T), In x n is the identity matrix of order n, JmqIn xn = diag[Jmq, Jmq,...,Jmq] where for i 0, m 0, Jm*q zi = qmzm-i, 0 i m and 0, otherwise.

2000 Mathematics Subject Classification: Primary 47B35,47B47.

Keywords: Hankel operators, inner functions, Hardy space.

 

 

 

 

 

 

 

 

 

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