We give sufficient conditions under which a weighted composition operator on Hilbert space of analytic functions is not weakly supercyclic. Also, we some necessary and for hypercyclicity supercyclicity operators the open unit disc.

For a positive integer m, bounded linear operator T on Hilbert space H is called an m-isometry, ifWe characterize all misometric unilateral weighted shift operators that are not m -1-isometries in terms of their weight sequences.Then we prove the reflexivity some classes operators: (1) All nonnegative powers m-isometric shifts.(2) The contractions whose spectrum closed unit disc.(3) non-negative hyponormal m-isometries. Introduction.Let be complex separable H, Lat lattice subspaces which...

Suppose that X is a separable normed space and the operators A Q are bounded on . In this paper, it shown if = , an isometry, nilpotent then operator + neither supercyclic nor weakly hypercyclic. Moreover, underlying Hilbert co‐isometric operator, we give sufficient conditions under which satisfies supercyclicity criterion.

By the well-known result of Yood, every strictly transitive algebra operators on a Banach space is WOT-dense. This motivated us to investigate relationships between SOT and WOT largeness sets transitivity behavior them. We show that, obtain Yood's result, strict may not be replaced by weaker condition hypertransitivity. prove for wide class topological vector spaces, SOT-dense set hypertransitive. The general form that are presented. also describe WOT-dense It shown hypertransitive if only...

An n-tuple of commuting operators, (T_1,T_2,...,T_n) on a Hilbert space \cal H is said to be hypercyclic, if there exists vector x \in such that the set {T_1^{k_1} T_2^{k_2}... T_n^{k_n}x : k_i \geq 0, i=1,2,...n} dense in H. In this paper, we give sufficient conditions under which adjoint an weighted composition operator analytic functions hypercyclic.

Let $\{\beta(n)\}$ be a sequence of positive numbers with $\beta(0) = 1$ and let $p\gt 0$. By the space $H^{p}(\beta)$, we mean set all formal power series $\sum^{\infty}_{n=0} \hat{f}(n) z^{n}$ for which |\hat{f}(n)|^{p} \beta(n)^{p} \lt \infty$. In this paper, study cyclic vectors forward shift operator supercyclic backward on $H^{p} (\beta)$.

A commuting $d$-tuple $T=(T_{1}, \ldots , T_{d})$ of bounded linear operators on a Hilbert space $\mathcal {H}$ is called spherical $m$-isometry if $\sum _{j=0}^{m}(-1)^{j}\binom {m}{j}Q_{T}^{j}(I)=0$, where $I$ denotes the identity operator and $Q_{T}(A)=\sum _{i=1}^{d}T_{i}^{*}AT_{i}$ for every $A$ {H}$. Also, $T$ toral _{p\in \mathbb {N}^{d},\, 0\leq p\leq n}(-1)^{\vert p\vert }\binom {n}{p}{T^{\ast }}^{p}T^{p}=0 $ all $n\in {N}^{d}$ with $\vert n\vert = m$. The present paper mainly...

An A-m-isometric operator is a bounded linear T on Hilbert space <TEX>$\mathcal{H}$</TEX> satisfying <TEX>$\sum\limits_{k=0}^{m}(-1)^{m-k}T^{*^k}AT^k=0$</TEX>, where A positive operator. We give sufficient conditions under which A-m-isometries are not N-supercyclic, for every <TEX>$N{\geq}1$</TEX>; that is, there subspace E of dimension N such its orbit dense in <TEX>$\mathcal{H}$</TEX>.

Let M_z and B denote, respectively, the multiplication operator backward shift on a weighted Hardy space. We present sufficient conditions so that M_{z^n} is similar to \bigoplus_1^nM_z, B^n \bigoplus_1^nB. The first part generalizes result obtained by Yucheng Li.

A bounded linear operator T on a Hilbert space ℋ , satisfying for every h ∈ is called convex operator. In this paper, we give necessary and sufficient conditions under which composition large class of weighted Hardy spaces an isometry. Also, discuss convexity multiplication operators.

A bounded linear operator T on a Hilbert space H is an (m, p) -isometry ifand m 1 .In this paper, two significant results will be proved.First, we introduce some perturbations of -isometries which are (n, for suitable n .Indeed, show that the sum and commuting nilpotent degree r (prp + m, every even number p .As application, second result to prove such operators not N -supercyclic any positive integer , if rational number.These generalize previous works -isometries.

A bounded linear operator $T$ on a Hilbert space is an isometric $N$-Jordan if it can be written as $A+Q$, where $A$ isometry and $Q$ nilpotent of order $N$ such that $AQ= QA$. In this paper, we will show the only weighted shift operators are isometries. This answers question recently raised.

Suppose that the multiplication operator by independent variable z, M z , acting on Banach spaces of formal Laurent series is invertible. We will use a result Hadwin and Nordgren to show reflexive. This improves recently obtained.

We present a non-weak supercyclicity criterion for vectors in infinite dimensional Banach spaces. Also, we give sufficient conditions under which class of weighted composition operators on space analytic functions is not weakly supercyclic. In particular, show that the semigroup linear isometries spaces $S^p$ ($p>1$), Moreover, observe every operator some such as disc algebra or Lipschitz

Using Banach algebra structure of the Hardy space, we describe all finite codimensional invariant subspaces a cyclic convolution operator on space $H^p$ unit disc for $1 \leq p \infty$. We also observe that every in commutant such operators is not weakly supercyclic.

In this note it is shown that there a bounded linear operator T on the Hardy Hilbert space H2 and vector f in such closure of set {αTnf:α∈ℂ,n≥0} not H2, but for every subsequence (nk)k=1∞ closed span {Tnkf:k≥1} whole H2. Furthermore, {Tng:n≥0} some g∈H2.

Let H be a separable complex Hilbert space. A commuting tuple <TEX>$T=(T_1,{\cdots},T_n)$</TEX> of bounded linear operators on is called spherical isometry if <TEX>$\sum_{i=1}^{n}T^*_iT_i=I$</TEX>. The T toral each <TEX>$T_i$</TEX> an isometry. In this paper, we show that for <TEX>$n{\geq}1$</TEX> there supercyclic n-tuple isometries <TEX>$\mathbb{C}^n$</TEX> and no or isometric infinite-dimensional

We characterize the commutants of some multiplication operators on a Banach space analytic functions defined bounded domain in plane. Under certain conditions symbol operator, we show that its commutant is set operators. This partially answers question Axler, Cuckovic and Rao. Next, hyper-reflexivity these are proved. The paper concluded by proving with symbols \varphi (z) = z^k, k=1, 2,... .