Yucheng li

Hebei Normal University · College of Mathematics and Information Science

Let \({\mathfrak{D}} \) be the Dirichlet space on the unit disc \({\mathbb{D}}\) and B(z) be the Blaschke product with n zero, and we prove that multiplication operator \(M_B\) on \({\mathfrak{D}}\) is similar to \(\bigoplus _{1}^{n}M_{z}\) on \(\bigoplus _{1}^{n}{\mathfrak{D}}\) by a crucial decomposition of \({\mathfrak{D}}.\) Two applications of...

Let \({{\mathbb {S}}}^{n}\) denote the unit sphere in \({\mathbb C}^{n}\). Let \(H^{2}({{\mathbb {S}}}^{n})\) be the standard Hardy space given by the closure in \(L^{2}({{\mathbb {S}}}^{n})\) of the polynomials in the coordinate functions of \(z_{1},\cdots , z_{n}\). For 2-tuple \(\{T_{1}, T_{2}\}\) acting on \(H^{2}({{\mathbb {S}}}^{2})\), we pro...

In this paper, we first show that the canonical solution operator \(S_1\) to \({\bar{\partial }}\) restricted to (0,1)-forms with holomorphic function coefficients can be expressed by an integral operator using the Dirichlet kernel. Then we prove that operator \(S_k\,(k\ge 1)\) is a Hilbert–Schmidt operator on the Dirichlet space of \({\mathbb {D}}...

In this paper we investigate the compact operators under Orlicz function, named noncommutative Orlicz sequence space (denoted by Sϕ(ℌ)), where ℌ is a complex, separable Hilbert space. We will show that the space generalizes the Schatten classes Sp(ℌ) and the classical Orlicz sequence space respectively. After getting some relations of trace and nor...

We consider the multiplication operator Mz1nz2n on a certain closed subspace La,α2++(Ar2) of weighted Bergman spaces La,α2(Ar2) over the biannulus Ar2. We prove that the operator Mz1nz2n is similar to ⨁1n2Mz1z2 on La,α2++(Ar2). Moreover, the reducing subspaces of Mz1nz2n are investigated.

In this paper, the definition of noncommutative Orlicz sequence spaces (denoted by S ϕ (H) is given, these spaces generalize the Schatten classes S p (H). After some relations of trace and norm on this spaces have been researched, one give the criterion of reflexivity of these spaces. At last, as an application, we find the Toeplitz operator x 1−|z...

In this paper, we study some connection between the compactness of radial operators and the boundary behavior of the corresponding Berezin transform on weighted Bergman spaces. More precisely, we prove that, under some mild condition, the vanishing of the Berezin transform on the unit circle is equivalent to the compactness of a class of radial ope...

Let g(z) be an n-degree polynomial (n≥2). Inspired by Sarason's result, we introduce the operator T1 defined by the multiplication operator Mg plus the weighted Volterra operator Vg on the Bergman space. We show that the operator T1 is similar to Mg on some Hilbert space Sg2(D). Then for g(z)=zn, by using matrix manipulations, the reducing subspace...

Let DD be the unit disk and SA(D)SA(D) denote the Sobolev disk algebra which consists of all analytic functions in the Sobolev space W2,2(D)W2,2(D). In this note, we prove that MznMzn is similar to ⨁1nMz on SA(D)SA(D). Then using the matrix manipulations combined with operator theory methods, we characterize the reducing subspaces of MznMzn on SA(D...

Let F-alpha(2)(alpha > 0) denote the Fock space which consists of all entire functions f in L-2(C, (A). We prove that the multiplication operator Me is quasi-similar to circle plus(n)(1) M-z on F. Then the reducing subspaces of M(z)n are characterized on F-alpha(2).

Let D be the unit disk and $A^{2}_{\alpha}(D)\,(\alpha > -1)$A^{2}_{\alpha}(D)\,(\alpha > -1) be the weighted Bergman space. In this paper, we prove that the multiplication operator MznM_{{z}^{n}} is similar to \mathop Å1n\mathop \oplus \limits _{1}^{n} M z on A2a(D)A^{2}_{\alpha}(D).

In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f(z) = z n g(z)(n ≥ 1), g(z) = b 0 + b 1 $ z^{p_1 } $ z^{p_1 } +b 2 $ z^{p_2 } $ z^{p_2 } +···, b k ≠ 0(k = 0, 1, 2, ...), our main result is $ M_{z^n } $ M_{z^n } )∩ $ M_{z^s } $ M_{z^s...

The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n + 1-Blaschke factors is unitary to n + 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we...

In this paper, by the Gelfand representation theory and the Silov idempotents theorem, we first obtain a central decomposition theorem related to a unital semi-simple n-homogeneous Banach algebra, and then give a similarity classification of two strongly irreducible Cowen-Douglas operators using this theorem.