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Vietnam Journal of Mathematics 36:4(2008) 373-386

 Complemented Subspaces in L(D)

Namita Das

Abstract.  In this paper we have shown that the little Bloch space B0 cannot be complemented in B and hence C() cannot be complemented in L(D). Further, we have obtained some closed subspaces of L(D) that can be complemented in L(D). As a consequence of these results we have shown {Tϕ: ϕ  h(D)} can be complemented in L(La2) and {hϕ: ϕ  h(D)} cannot be complemented in L(La2, ()0). Here Tϕ is the Toeplitz operator on the Bergman space La2, hϕ is the little Hankel operator from La2 into (0 = {:  , f(0) = 0} and h(D) is the space of bounded harmonic functions on the unit disk D.

 

2000 Mathematics Subject Classification: 47B35, 47B38.

Keywords: Complemented subspace, Toeplitz operators, Hankel operators, Bergman space, Bloch space.

 

 

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