18 Article(s)

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Document(s)

Title

As is well known, for any operator $T$ on a complex separable Hilbert space, $T$ has the polar decomposition $T=U|T|$, where $U$ is a partial isometry and $|T|$ is the nonnegative operator $(T^*T)^{\frac{1}{2}}$. In 2014, Tian et al. proved that on a...

Let $\mathcal{H}$ be a complex separable Hilbert space. We prove that if $\{f_{n}\}_{n=1}^{\infty}$ is a Schauder basis of the Hilbert space $\mathcal{H}$, then the angles between any two vectors in this basis must have a positive lower bound. Furthe...

Let $\mathcal{H}$ be a complex separable Hilbert space. We prove that if $\{f_{n}\}_{n=1}^{\infty}$ is a Schauder basis of the Hilbert space $\mathcal{H}$, then the angles between any two vectors in this basis must have a positive lower bound. Furthe...

In this paper we show a Cowen-Douglas operator $T \in \mathcal{B}_{n}(\Omega)$ is the adjoint operator of some backward shift on a general basis by choosing nice cross-sections of its complex bundle $E_{T}$. Using the basis theory model, we show that...

As is well-known, each positive operator $T$ acting on a Hilbert space has a positive square root which is realized by means of functional calculus. However, it is not always true that an operator have a square root. In this paper, by means of Schaud...