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Content available remote Pochodne instrumenty finansowe w zarządzaniu ryzykiem w bankach korporacyjnych
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nr 4
37-49
PL
Pochodne instrumenty finansowe wprowadzono na globalnych rynkach finansowych w celu zmniejszenia ryzyka. Aktualnie wykorzystanie pochodnych instrumentów finansowych przez polskie banki korporacyjne dynamicznie wzrasta. Właściwe ich wykorzystanie umożliwia sprawne i skuteczne zarządzanie ryzykiem oraz przyczynia się do polepszenia kondycji finansowej banków. Banki wykorzystują instrumenty pochodne w celu zabezpieczenia się przed ryzykiem oraz dla jego ograniczenia i optymalizacji. Zarządzanie ryzykiem w banku stanowi integralną część zarządzania strategicznego instytucją finansową. Działania banków za pomocą instrumentów pochodnych są nierozerwalnym elementem ich polityki wewnętrznej.
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Content available remote Derivable maps and generalized derivations on nest and standard algebras
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tom Vol. 49, nr 3
331--344
EN
For an algebra A, an A-bimodule M, and m (…) M, define a relation on A by RA(m, 0) = {(a, b) (…) A x A : amb = 0}. We show that generalized derivations on unital standard algebras on Banach spaces can be characterized precisely as derivable maps on these relations. More precisely, if A is a unital standard algebra on a Banach space X then (…)L(A,B(X)) is a generalized derivation if and only if (..) is derivable on RA(M,0), for some M (…) B(X). We give an example to show this is not the case in general for nest algebras. On the other hand, for an idempotent P in a nest algebra A = algN on a Hilbert space H such that P is either left-faithful to N or right-faithful to N﬩, if δ (…)L(A, B)H)) is derivable on RA(P, 0) then δ is a generalized derivation.
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Content available remote Pairs of derivations on rings and Banach algebras
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tom Vol. 41, nr 2
297-308
EN
We give a generalization of Vukman's theorem concerning a pair of derivations on rings. Then applying this purely algebraic result we obtain several range inclusion results of pair of derivations on Banach algebras.
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Content available remote Derivation with engel conditions on multilinear polynomials in prime rings
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2009
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tom Vol. 42, nr 3
467-478
EN
Let R be a prime ring with extended centroid C and characteristic different from 2, d a nonzero derivation of R, f(x1,..., xn) a nonzero multilinear polynomial over C such that [d2(f(x1,... , xn)),d(f(x1,... ,xn))]k = 0 for all x1,... ,xn in some nonzero right ideal [...] of R, where k is a fixed positive integer. If d(p) p [..]0, then pC = eRC for some idempotent e in the socle of RC and /(x1,..., xn) is central-valued on eRCe.
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Content available remote On (m, n)-derivations of some algebras
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tom Vol. 47, nr 3
672--694
EN
Let A be a unital algebra, δ be a linear mapping from A into itself and m, n be fixed integers. We call δ an (m, n)-derivable mapping at Z, if mδ(AB) + nδ(BA) = mδ(A)B + mAδ(B) + nδ(B)A + nBδ(A) for all A, B (…) A with AB = Z. In this paper, (m, n)-derivable mappings at 0 (resp. IA (…) 0, I) on generalized matrix algebras are characterized. We also study (m, n)-derivable mappings at 0 on CSL algebras. We reveal the relationship between this kind of mappings with Lie derivations, Jordan derivations and derivations.
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Content available remote Generalized finite operators
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tom Vol. 38, nr 1
163--167
EN
Let B(H) be the algebra of all bounded linear operators on an infinite dimensional complex and separable Hilbert space H. A infinity B(H) is called finite if \\AX - XA - I\\ > 1, VX infinity B(H). In this paper we extend the class of finite operators to a more general class of pairs of operators called generalized finite operators defined by {(A, B) infinity B(H) x B(H) : \\AX - XB - I\\ > 1, VX infinity B(H)} and we present some pairs of generalized finite operators.
EN
Environmental pollution causes a variety of health problems, including cancer. Many known pollutants have carcinogenic properties and polycyclic aromatic hydrocarbons (PAH) belong to this group. In this study, an in vitro culture of V79 cells of the Chinese hamster was subjected to three tested PAHs: 5-amino-2,3-dihydro-1H-cyclopenta-[c]phenanthrene (ACP[c]Ph), 5-amino-9-methoxy-2,3-dihydro-1H-cyclopenta[c]phenanthrene (AMCP[c]Ph) and cyclopenta[c]phenanthrene (CP[c]Ph). The in vitro micronucleus (MN) assay was applied in order to evaluate the genotoxic properties of the studied compounds. The highest genotoxic effect was observed for AMCP[c]Ph in a concentration of 0.02μg·ml-1. The genotoxic effect of the other two compounds was slightly lower.
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Content available remote Identities with generalized derivations in semiprime rings
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EN
Let R be a semiprime ring. An additive mapping F:R  R is called a generalized derivation of R if there exists a derivation d : R  R such that F(xy) = F(x)y + xd(y) holds, for all x,y  R. The objective of the present paper is to study the following situations: (1) (...), for all x, y in some appropriate subset of R.
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Content available remote On some equations related to derivations in rings and Banach algebras
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EN
The main purpose of this paper is to investigate additive mapping D : R -> R, where R is a (m + n +1)! and \m2 + n2 - m - n - 4mn\ -torsion free semiprime ring with the identity element, satisfying the relation 2D(xm+n+l) = (m+-n+1)(xmD(x)xn +-xnD(x)xm), for all is an element of R and some integers m > 1, n > 1, m2 + n2 - m - n - 4mn /=0.
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Content available remote Approximation of additive functional equations in NA Lie C*-algebras
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tom Vol. 51, nr 1
37--44
EN
In this paper, by using fixed point method, we approximate a stable map of higher *-derivation in NA C*-algebras and of Lie higher *-derivations in NA Lie C*-algebras associated with the following additive functional equation [wzór], where m ≥ 2.
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Content available remote On derivations of operator algebras with involution
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tom Vol. 47, nr 4
784--790
EN
The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X) be an algebra of all bounded linear operators on X and let A(X) (…) L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D : A(X) → L(X) satisfying the relation 2D(AA*A) = D(AA*)A + AA*D(A) + D(A)A*A + AD(A*A) for all A (…) A(X). In this case, D is of the form D(A) = [A,B] for all A (…) A(X) and some fixed B (…) L(X), which means that D is a derivation.
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Content available remote On alfa-derivations of prime and semiprime rings
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tom Vol. 38, nr 2
283--290
EN
In this paper we investigate identities with alfa-derivations on prime and semiprime rings. We prove, for example, the following result. If D : R - R is an alfa-derivation of a 2 and 3-torsion free semiprime ring R such that [D(x},x2] = 0 holds, for all x is an element of R, then D maps R into its center. The results of this paper are motivated by the work of Thaheem and Samman [20].
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