Let B(X) and Mn (F) be the algebra of all bounded Linear operators on a complex Banach space X with dimX³3 and the algebra of all n×n matrices over a field F with F¹2, respectively. Also let F(A)be the space of all fixed points of an operator AÎB(X). In this paper, we characterize the forms of Linear maps f:B(X)®B(X) which satisfy F(A)=0ÛF(f(A))=0 and Linear maps f: Mn(F)® Mn(F) which preserve the fixed points of matrices.

We survey some results about invertibility and spectrum preserving Linear maps on the algebra of all bounded operators on a Banach space or more generally on Banach algebras.

The post-black playwright, Marcus Gardley has been concerned with the concept of African American identity as defined within the nexus of diverse socio-cultural elements. This study explores the role of religion as an integral and indispensable constituent of African American identity in three of Gardley’s plays, namely, And Jesus Moonwalks the Mississippi, The House That Will Not Stand, and A Wolf in Snake Skin Shoes, while considering the relevant cultural and sociological studies on the role of religion in African American communities. Drawing upon the conception of identity in the framework of African American criticism, the focus of this paper is on Gardley’s intricate portrayal of the function of church and religious beliefs in shaping black identity. It is argued that Gardley’s insightful and multilayered depiction of religion in his drama delineates a rather complex and paradoxical function where African American identity both benefits from, and bears the negative impacts of, religiosity. This study reveals that, in Gardley’s plays, Christianity sometimes acts as a soothing balm to African Americans who have for long fought not only racial discrimination but also collective and individual traumas in various stages of their lives, as in the cases of Free, Maud Lynn and Miss Ssippi. In some cases, however, a type of Christianity promoted by the black church is presented as an obstacle in the way of some African Americans’ recognition of their true identity, as observed in the case of Gumper.

The importance of animal figure is dramatic in Iranian art since ancient time. Animal figures were sometimes used as symbols of agriculture and nutrition and also as symbols of gods, kingdoms and elements of universe. Among animal figures, wild goat figure has a great importance. In ancient times this figure was symbol of seeking rain and blessing rather than just being a decorative figure.After Sassanid era and in Islamic age wild goat figure lost its importance and was mainly preserved in rural and nomadic hand-woven due to fundamental changes in beliefs as well as artistic and cultural attitudes.In this essay we tend to seek the reasons behind perseverance and persistence of wild goat figure in Iranian art and its meaning by investigating the available figures from prehistory until today, and comparing them to each other through an analytic way.It seems that wild goat figure’s formation on stones was due to ancient peoples beliefs and costumes which considered this figure as a symbol of rain, fertility and abundance. This figure was passed from each generation to next in ancient art and was protected from changes and damages of the time through nomadic hand-woven.The correlation between this figure and life, livelihood, dreams of the weaver and the traditional way of its transmission within centuries is the cause of its persistence among today’s nomadic weavings.Today’s weaver is a preserver of this figure without knowing its exact meaning and that’s how the rug contains an ancient figure and desire.

For X, Y Î Mnm (:= Mnm(R)), we say X is weakly matrix majorized or matrix majorized from the left by Y and write X <e Y , if X = RY for some row stochastic matrix R. Also we write X ~e Y if X <e Y <e X. A mapping T: Mnm → Mnm is said to be a strong preserver of <e, if {X Î Mnm: X <e A} = {X Î Mnm: TX <e TA} for all A Î Mnm. Two such strong preservers T and Τ are called equivalent if TX ~e Τ X for all X Î Mnm. It is shown that if m≥ 2 and if T: Mnm → Mnm is a surjective (not necessarily Linear) strong preserver of <e, then T −T0 is equivalent to a Linear strong preserver of <e.

Let Mn,m be the set of all n´m matrices with entries in F, where F is the field of real or complex numbers. A real or complex n´n matrix is generalized row stochastic (g-row stochastic) if all of its row sums equal one. For X, YÎMn,m , we say that Y is right gw-majorized by X and write X >rgw Y if Y=XR for some g-row stochastic matrix R. Here, we characterize all strong Linear preservers of >rgw on Mn,m.

Let Mm, nMm, n be the set of all mm-by-nn real matrices. A matrix RR in Mm, nMm, n with nonnegative entries is called strictly sub row stochastic if the sum of entries on every row of RR is less than 1. For A, B∈ Mm, nA, B∈ Mm, n, we say that AA is strictly sub row Hadamard majorized by BB (denoted by A≺ SHB)A≺ SHB) if there exists an mm-by-nn strictly sub row stochastic matrix RR such that A=R∘ BA=R∘ B where X∘ YX∘ Y is the Hadamard product (entrywise product) of matrices X, Y∈ Mm, nX, Y∈ Mm, n. In this paper, we introduce the concept of strictly sub row Hadamard majorization as a relation on Mm, nMm, n. Also, we find the structure of all Linear operators T: Mm, n→ Mm, nT: Mm, n→ Mm, n which are preservers (resp. strong preservers) of strictly sub row Hadamard majorization.

Cappadocia which was located in Asia Minor was the main battlefield of Greeks and Achaemenids, particularly during the last years of Achaemenid rule and could change the power balance between the two states by supporting each one. During the Achaemenid era, some of Achaemenid family had been appointed as the rulers of Cappadocia and after the fall of the Achaemenids, this Satrapy became a base for the commanders who wanted to defend against Alexander and his successors. Since parts of Kingdom route passed over Cappadocia and this province was adjacent to the sea, this position gave more importance to Cappadocia. Yet, no single and comprehensive research has been conducted on the role of the Cappadocia in maintenance of the Achaemenid culture and tradition in Asia Minor. Using historical research method, historical evidences and archeological results, this paper attempts to investigate the geographical limits and position of the Cappadocia in Achaemenid era and its role in the maintenance of the culture and tradition of the Achaemenids in Asia Minor after the fall of Achaemenid kingdom.

The aim of this work is to characterize all bounded Linear operators $T:\lpi\rightarrow\lpi$ which preserve disjoint support property. We show that the constant coefficients of all isometries on $\lpi$ are in the class of such operators, where $2\neq p\in [1,\infty )$ and $I$ is a non-empty set. We extend preserving disjoint support property to Linear operators on $\mathfrak{c}_{0}(I).$ At the end, we obtain some equivalent properties of isometries on Banach spaces.