Some remarks on derivations in semiprime rings and standard operator algebras

In this paper identities related to derivations on semiprime rings and standard operator algebras are investigated. We prove the following result which generalizes a classical result of Chernoff. Let X be a real or complex Banach space, let L(X) be the algebra of all bounded linear operators of X into itself and let A(X) L(X) be a standard operator algebra. Suppose there exists a linear mapping D:A(X)→ L(X) satisfying the relation 2D(A3)=D(A2)A+A2D(A)+D(A)A2+AD(A2) for all A A(X). In this case D is of the form D(A)=AB-BA for all A A(X) and some fixed B L(X), which means that D is a linear derivation

Identities with derivations on rings and Banach algebras

In this paper we prove the following result. Let m 1, n 1 be integers and let R be a 2mn(m+n-1)!-torsion free semiprime ring. Suppose there exist derivations D, G : R R such that D(xm)xn + xnG(xm) = 0 holds for all x R. In this case both derivations D and G map R into its center and D = -G. We apply this purely algebraic result to obtain a range inclusion result of continuous derivations on Banach algebras

Border, identity, everyday life: The South Slavs of Gara in state security documents (1945–1956)

The Baja Triangle, also known as Northern Bácska, geographically roughly included the area between Baja (in Hungary), Subotica and Sombor (in Serbia). It has been a multiethnic region for centuries, inhabited by Hungarians, Germans, and South Slavs. The physical proximity of the border and its separating function had a fundamental impact on the daily lives of the Hungarians and South Slavs living here, especially after 1948, when, because of the escalation of the Soviet-Yugoslav conflict, Hungarian-Yugoslav relations also became frosty. In my paper, I will examine how the fluctuating Hungarian–Yugoslav relations following World War Two affected the South Slavs living there in connection with Gara, a multiethnic village close to the Hungarian–Yugoslav border, how it affected their everyday life, their ideas about the border, their identity and their relationship with other nationalities

On functional equations related to bicircular projections

In this paper we prove the following result. Let R be a 2-torsion free semiprime *-ring. Suppose that D, G : R → R are additive mappings satisfying the relations D(xyx) = D(x)yx + xG(y*)*x + xyD(x), G(xyx) = G(x)yx + xD(y*)*x + xyG(x), for all pairs x, y ∈ R. In this case D and G are of the form 8D(x) = 2(d(x) + g(x)) + (p + q)x + x(p + q), 8G(x) = 2(d(x) - g(x)) + (q - p)x + x(q - p), for all x ∈ R, where d, g are derivations of R and p, q are some elements from symmetric Martindale ring of quotients of R. Besides, d(x) = -d(x*)*, g(x) = g(x*)*, for all x ∈ R, and p* = p, q* = -q

Jugoszlávia elleni szovjet katonai támadás lehetősége a brit források tükrében, 1948-1953

Although the hypothetical possibility of Soviet and/or satellite military attack against Yugoslavia first emerged after the Kominform resolution in Bucharest (June 1948) among the views of the British Foreign Office, they only became fully occupied with this question from 1949 on, as a result of the ever increasing border incidents, the Soviet note of 18 August 1949, which was considered as an ultimatum by the Yugoslav leaders, and the outbreak of the Korean War in 1950. The analyses did not exclude the possibility of a direct military attack, they only took it into consideration as the last possibility, in case the Soviet Union would have risked the outbreak of World War III, or would have wanted to save her prestige in Eastern Europe because of the protraction of the Korean War. From 1950 on, the analyses foresaw four possibilities regarding the Soviet Union: „wait and see" strategy, organising internal revolts, guerilla warfare and direct military attack, which was considered to be the least probable, even if numerous ambassadors and military attachés analysed the process and the consequences of this possibility, sometimes contradicting each other. The question of military attack against Yugoslavia was on the agenda during Foreign Secretary Eden's visit in Yugoslavia in 1952 and Tito's visit in London in March 1953, yet no change occurred in its judgement. On the one hand, Yugoslavia was interested in keeping the question on the agenda of discussions with Western leaders as she wanted the obtain Western military help. On the other hand, the Foreign Office estimated no change in Soviet foreign policy after Stalin's death, and therefore, they didn't consider the military attack against Yugoslavia real, but they did make an effort to integrate her into their own defence system