1. Cui, Jianlian; Hou, Jinchuan: Linear maps on von Neumann algebras preserving zero products of tr-rank. (English). - [J] Bull. Aust. Math. Soc. 65, No.1, 79-91(2002). [ISSN 0004-9727]Matej Brešar, 2005, review, book review, critique Keywords: matematika, teorija operatorjev, linearni ohranjevalci, von Neumannove algebre, ničelni produkt, mathematics, operator theory, Banach algebras, linear preservers, von Neumann algebra, zero product, tr-rank
Published in DKUM: 16.07.2015; Views: 1380; Downloads: 20
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2. A note on spectrum-preserving mapsJ. Alaminos, Matej Brešar, Peter Šemrl, A. R. Villena, 2012, original scientific article Abstract: Naj bosta ▫$A$▫ in ▫$B$▫ enotski polenostavni Banachovi algebri. Če je ▫$phi colon M_2(A)to B$▫ bijektivna linearna preslikava, ki ohranja spekter, potem je ▫$phi$▫ jordanski homomorfizem.
Keywords: matematika, teorija operatorjev, ohranjevalec spektera, Banachova algebra, jordanski homomorfizem, mathematics, operator theory, spectrum-preserving map, Banach algebra, Jordan homomorphism
Published in DKUM: 10.07.2015; Views: 1528; Downloads: 114
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3. Characterizing Jordan maps on C [ast]-algebras through zero productsJ. Alaminos, Matej Brešar, J. Extremera, A. R. Villena, 2010, original scientific article Abstract: Naj bosta ▫$A$▫ in ▫$B$▫ ▫$C^ast$▫-algebri, ▫$X$▫ naj bo bistveni Banachov ▫$A$▫-bimodul in naj bosta ▫$T colon A to B$▫ in ▫$S colon A to X$▫ zvezni linearni preslikavi; ▫$T$▫ naj bo surjektivna. Denimo, da je ▫$T(a)T(b) + T(b)T(a) = 0$▫ in ▫$S(a)b + bS(a) + aS(b) + S(b)a = 0$▫, kadarkoli ▫$a, b in A$▫ zadoščata ▫$ab = ba = 0$▫. Dokažemo, da je ▫$T = wPhi$▫ in ▫$S = D + wPsi$▫, kjer ▫$w$▫ leži v centru multiplikatorske algebre ▫$B$▫, ▫$Phicolon A to B$▫ je jordanski epimorfizem, ▫$D colon A to X$▫ je odvajanje in ▫$Psi colon A to X$▫ je bimodulski homomorfizem.
Keywords: matematika, teorija operatorjev, ▫$C^ast$▫-algebra, homomorfizem, jordanski homomorfizem, odvajanje, jordansko odvajanje, ohranjevalec ničelnega produkta, mathematics, operator theory, ▫$C^ast$▫-algebra, homomorphism, Jordan homomorphism, derivation, Jordan derivation, zero-product-preserving map
Published in DKUM: 10.07.2015; Views: 1114; Downloads: 47
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4. Maps preserving zero productsJ. Alaminos, Matej Brešar, J. Extremera, A. R. Villena, 2009, original scientific article Abstract: Linearna preslikava ▫$T$▫ iz Banachove algebre ▫$A$▫ v Banachovo algebro ▫$B$▫ ohranja ničelni produkt, če je ▫$T(a)T(b) = 0$▫, kadarkoli je ▫$ab = 0$▫. Glavna tema članka je vprašanje, kdaj je zvezna linearna surjektivna preslikava ▫$T: A to B$▫, ki ohranja ničelni produkt, uteženi homomorfizem. Dokažemo, da to velja za velik razred algeber, ki vključuje grupne algebre. Naša metoda sloni na obravnavi bilinearnih preslikav ▫$phi : A times A to X$▫ (kjer je ▫$X$▫ Banachov prostor) z lastnostjo, da iz ▫$ab=0$▫ sledi ▫$phi(a,b) = 0$▫. Dokažemo, da taka preslikava zadošča ▫$phi(amu, b) = phi(a,mu b)$▫ za vse ▫$a,b in A$▫ in vse ▫$mu$▫ iz zaprtja glede na krepko operatorsko topologijo podalgebre multiplikacijske algebre ▫${mathcal M}(A)$▫ generirane z dvostranko potenčno omejenimi elementi. Ta metoda je uporabna tudi za karakterizacijo odvajanj s pomočjo ničelnega produkta.
Keywords: matematika, teorija operatorjev, grupna algebra, ▫$C^ast$▫-algebra, homomorfizem, uteženi homomorfizem, odvajanje, posplošeno odvajanje, mathematics, operator theory, group algebra, ▫$C^ast$▫-algebra, homomorphism, weighted homomorphism, derivation, generalized derivation, separating map, disjointness preserving map, zero product preserving map, doubly power-bounded element
Published in DKUM: 10.07.2015; Views: 1301; Downloads: 99
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5. Jacob, Birgit; Trunk, Carsten: Location of the spectrum of operator matrices which are associated to second order equations. (English). - [J] Oper. Matrices 1, No. 1, 45-60 (2007). [ISSN 1846-3886]Miklavž Mastinšek, 2008, review, book review, critique Keywords: matematika, teorija operatorjev, linearni operatorji, spekter, mathematics, operator theory, stiffness operator, damping operator, essential spectrum, semigroup generator
Published in DKUM: 10.07.2015; Views: 1043; Downloads: 21
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6. Bertoldi, Marcello; Fornaro, Simona; Lorenzi, Luca: Pointwise gradient estimates in exterior domains. (English). - [J] Arch. Math. 88, No. 1, 77-89 (2007). [ISSN 0003-889X; ISSN 1420-8938]Miklavž Mastinšek, 2007, review, book review, critique Keywords: matematika, parcialne diferencialne enačbe, teorija operatorjev, neomejeni koeficienti, problem Cauchy-Neumanna, polgrupe Markova, mathematics, partial differential equations, operator theory, functional differential equation, unbounded coefficients, Cauchy-Neumann problem, Markov semigroup
Published in DKUM: 10.07.2015; Views: 1509; Downloads: 43
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7. Voigt, Jürgen: The modulus semigroup for linear delay equations II. (English). - [J] Note Mat. 25, No. 2, 191-208 (2006).[ISSN 1123-2536; ISSN 1590-0932]Miklavž Mastinšek, 2007, review, book review, critique Keywords: matematika, navadne diferencialne enačbe, teorija operatorjev, funkcijska diferencialna enačba, teorija perturbacij, mathematics, ordinary differential equations, operator theory, functional differential equation, modulus semigroup, perturbation theory
Published in DKUM: 10.07.2015; Views: 1766; Downloads: 37
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8. Zero product preserving maps on C[sup]1 [0,1]J. Alaminos, Matej Brešar, Miran Černe, J. Extremera, A. R. Villena, 2008, original scientific article Abstract: Glavni rezultat članka karakterizira zvezne bilinearne preslikave ▫$phi$▫ iz ▫$C^1[0,1] times C^1[0,1]$▫ v Banachov prostor ▫$X$▫ z lastnostjo, da iz ▫$fg=0$▫ sledi ▫$phi(f,g) = 0$▫. Ta rezultat se uporabi pri študiju ohranjevalcev ničelnega produkta na ▫$C^1[0,1]$▫ in pri študiju operatorjev na ▫$C^1[0,1]$▫, ki zadoščajo neki verzijo pogoja o lokalnosti operatorja.
Keywords: matematika, teorija operatorjev, zvezne odvedljive funkcije, bilinearni ohranjevalci ničelnega produkta, linearni ohranjevalci ničelnega produkta, lokalni operator, mathematics, operator theory, continuously differentiable functions, zero product preserving bilinear map, zero product preserving linear map, local operator
Published in DKUM: 10.07.2015; Views: 1192; Downloads: 48
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9. Lee, Tsiu-Kwen: Derivations on noncommutative Banach algebras. (English). - [J] Stud. Math. 167, No.2, 153-160 (2005). [ISSN 0039-3223; ISSN 1730-6337]Matej Brešar, 2006, review, book review, critique Keywords: matematika, teorija operatorjev, odvajanje, kvazinilpotentnost, Banachova algebra, Jacobsonov radikal, prakolobar, polenostavni kolobarji, mathematics, operator theory, derivation, quasinilpotent, Banach algebra, Jacobson radical, prime ring, semisimple ring
Published in DKUM: 10.07.2015; Views: 1166; Downloads: 28
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10. Duggal, B.P.: On the range closure of an elementary operator. (English). - [J] Linear Algebra Appl. 402, 199-206 (2005). [ISSN 0024-3795]Matej Brešar, 2006, review, book review, critique Keywords: matematika, teorija operatorjev, Hilbertov prostor, elementarni operator, skrčenje, posplošeni skalarni operator, mathematics, operator theory, Hilbert space, elementary operator, contraction, generalized scalar operator, single-valued extension property, SVEP
Published in DKUM: 10.07.2015; Views: 1195; Downloads: 53
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