Abstract. In this article, we provide a sufficient condition which gives Devaney chaos and distributional chaos for Cowen-Douglas operators. In fact, we obtain a distributionally chaotic criterion for bounded linear operators on Banach spaces.
Abstract. In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators T Φ , where Φ = F +G * , F (z), G(z) are some matrix valued polynomials on the vector valued Bergman space L 2 a (D, C n ). We also show some necessary conditions for the hyponormality of T F +G * with F + G * ∈ h ∞ ⊗ M n×n on L 2 a (D, C n ).
We completely characterize the finite rank semicommutators, commutators, and zero product of block Toeplitz operatorsTFandTGwithF,G∈h∞⊗Mn×non the vector valued Bergman spaceLa2(𝔻,ℂn).
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