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 {T_ϕ: ϕ h^∞(D)} can be complemented in L(L_a²) and {h_ϕ: ϕ h^∞(D)} cannot be complemented in L(L_a², ()₀). Here T_ϕ is the Toeplitz operator on the Bergman space L_a², h_ϕ is the little Hankel operator from L_a² 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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