This paper focuses on the binormality of block Toeplitz operators with matrix valued circulant symbols. We also study some Γ-dilations of Toeplitz operators. Moreover, we also analyze the invariant subspace of Toeplitz operators with matrix-valued symbols.

A bounded linear operator T : H H is a C -hyponormal operator if T * T -CT T * C 0 for a conjugation C on H .In this paper, we study properties of C -hyponormal operators.Especially, we prove that for M Lat(T ) and a conjugationFinally, we prove that if T * is p -hyponormal for 0 < p 1 and C is a conjugation on H , then T is C -hyponormal if and only if T is normal.

Abstract In this paper, we investigate properties of hyponormal Toeplitz operators whose symbols are analytic or co-analytic on a Newton space. We establish both necessary and sufficient conditions for a Toeplitz operator $$T_{\phi }$$ $T_{\phi }$ to be hyponormal or normal. Additionally, we give some applications of such results.