Related papers: Operators on (C[0,1]) preserving copies of asympto…

It is shown that if $\alpha ,\zeta $ are ordinals such that $1\leq \zeta <\alpha <\zeta \omega ,$ then there is an operator from $C(\omega ^{\omega ^\alpha })$ onto itself such that if $Y$ is a subspace of $C(\omega ^{\omega ^\alpha })$…

It is proved that every operator from a weak$^*$-closed subspace of $\ell_1$ into a space $C(K)$ of continuous functions on a compact Hausdorff space $K$ can be extended to an operator from $\ell_1$ to $C(K)$.

The main result is that the commutators on $\ell_1$ are the operators not of the form $\lambda I + K$ with $\lambda\neq 0$ and $K$ compact. We generalize Apostol's technique (1972, Rev. Roum. Math. Appl. 17, 1513 - 1534) to obtain this…

We give sufficient conditions on an asymptotic $\ell_p$ (for $1 < p < \infty$) Banach space which ensure the space admits an operator which is not a compact perturbation of a multiple of the identity. These conditions imply the existence of…

Suppose $\Pi_1(E, F)$ is the space of all absolutely 1-summing operators between two Banach spaces $E$ and $F$. We show that if $F$ has a copy of $c_0$, then $\Pi_1(E, F)$ will have a copy of $c_0$, and under some conditions if $E$ has a…

Let $E$ be a real Banach space. For $x,y \in E,$ we follow R.James in saying that $x$ is orthogonal to $y$ if $\|x+\alpha y\|\geq \|x\|$ for every $\alpha \in R$. We prove that every operator from $E$ into itself preserving orthogonality is…

We introduce a class of operators on $L_1$ that is stable under taking sums of pointwise unconditionally convergent series, contains all compact operators and does not contain isomorphic embeddings. It follows that any operator from $L_1$…

We study linear operators preserving the property of being a volume polynomial. More, precisely we show that a linear operator preserves this property if the associated symbol is itself a volume polynomial. This can be seen as an analogue…

There exist injective Tauberian operators on $L_1(0,1)$ that have dense, non closed range. This gives injective, non surjective operators on $\ell_\infty$ that have dense range. Consequently, there are two quasi-complementary, non…

Unlike for $\ell_p$, $1<p\leq\infty$, the discrete Ces\`aro operator $C$ does not map $\ell_1$ into itself. We identify precisely those weights $w$ such that $C$ does map $\ell_1(w)$ continuously into itself. For these weights a complete…

We give a characterization of the compact operators on a model space in terms of asymptotic Toeplitz operators.

It is proved that for every stratifiable space $Y$ and a closed subset $X\subset Y$ there exists a regular (i.e. linear positive with unit norm) extension operator $T:C(X\times X)\to C(Y\times Y)$ preserving the class of (pseudo)metrics.…

A recent result of Freeman, Odell, Sari, and Zheng states that whenever a separable Banach space not containing $\ell_1$ has the property that all asymptotic models generated by weakly null sequences are equivalent to the unit vector basis…

In previous work of C. A. Tracy and the author asymptotic formulas were derived for certain operator determinants whose interest lay in the fact that quotients of them gave solutions to the cylindrical Toda equations. In the present paper…

By a completion of a lemma of Babalola and Opoola \cite{KT}, we prove that certain generalized integral operators preserve $n$-starlikeness in the open unit disk $E=\{z\in \mathbb{C}: |z|<1\}$. Our results generalize, extend and improve…

A Banach space contains asymptotically isometric copies of $\ell_1$ if and only if its dual space contains an isometric copy of $L_1$.

We derive asymptotic information on the iterates of a Volterra convolution operator acting on L^p(0,1), subject to a mild smoothness condition on the kernel. In particular, an asymptotically equal sequence of rank 1 operators is obtained,…

We present condition on higher order asymptotic behaviour of basic sequences in a Banach space ensuring the existence of bounded non-compact strictly singular operator on a subspace. We apply it in asymptotic $\ell_p$ spaces, $1\leq…

We investigate the structure of norm-preserving and linear but not necessarily surjective operators on variable-exponent, discrete Lebesgue spaces. A certain class of isometries, novel to this work, are especially considered; this class…

Let $E(0,1)$ be a symmetric space on $(0,1)$ and $C_F$ be a symmetric ideal of compact operators on the Hilbert space $\ell_2$ associated with a symmetric sequence space $F$. We give several criteria for $E(0,1)$ and $ F$ so that $E(0,1)$…