In this paper we introduce the notion of $varphi$-commutativity for a Banach algebra $A$, where $varphi$ is a continuous homomorphism on $A$ and study the concept of $varphi$-weak amenability for $varphi$-commutative Banach algebras. We give an example to show that the class of $varphi$-weakly amenable Banach algebras is larger than that of weakly amenable commutative Banach algebras. We charac...

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.

A series of cobalt complexes with pentadentate pyridine-rich ligands is studied. An initial Co(II) amine complex 1 is prone to aerial oxidation yielding a Co(III) imine complex 2 that is further converted into an amide complex 4 in presence of adventitious water. Introduction of an N-methyl protecting group to the ligand inhibits this oxidation and gives rise to the Co(II) species 5. Both the C...

Eg̃eciog̃lu and Remmel [2] gave an interpretation for the entries of the inverse Kostka matrix K in terms of special rim-hook tableaux. They were able to use this interpretation to give a combinatorial proof that KK = I but were unable to do the same for the equation KK = I. We define a sign-reversing involution on rooted special rim-hook tableaux which can be used to prove that the last column o...

Hot-electron transport in Co/Cu/Co trilayer films has been studied in the energy range from 1.0 to 2.0 eV using ballistic electron magnetic microscopy. Both the spin-dependent attenuation lengths of Co and the cumulative polarizing effects of spin-dependent tunneling and transmission across a Co/Cu interface have been determined. For very thin (a few A) Co layers, the latter effects result in a...

The main result is the following. Let f:X→Y be a continuous mapping of completely Baire space X onto hereditary weakly Preiss-Simon regular Y such that image every open subset resolvable set in Y. Then Baire. classical Hurewicz theorem about closed embedding rational numbers into metrizable spaces generalized to spaces.

I take the first part of the title of my essay from a character in Mary Wroth’s Urania , dubbed the Lady of the Oddest Passion, who makes a fleeting appearance in book 3. 1 This lady, described as “most loving, most discreet” (452), is loved by, and in return loves equally, two men. All three were content with this situation for a time, but ultimately the Lady is pressed to choose between the s...

In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It was proved that a pairwise weakly Lindelof property is not a hereditary property.

This article examines explanations for both Internet use and non-use by older individuals. Older adults are often considered a homogeneous group with uniform reasons for Internet non-use, or when they are online, practising a uniform range of activities. The study gathered data concerning senior non-users through a national telephone survey. Data concerning senior Internet users were obtained t...