In this paper $LJ$-spaces are introduced and studied. They are a common generalization of Lindelöf spaces and $J$-spaces researched by E. Michael. A space $X$ is called an $LJ$-space if, whenever $\lbrace A,B\rbrace $ is a closed cover of $X$ with $A\cap B$ compact, then $A$ or $B$ is Lindelöf. Semi-strong $LJ$-spaces and strong $LJ$-spaces are also defined and investigated. It is demonstrated that the three spaces are different and have interesting properties and behaviors.
We characterize statistical independence of sequences by the $L^p$-discrepancy and the Wiener $L^p$-discrepancy. Furthermore, we find asymptotic information on the distribution of the $L^2$-discrepancy of sequences.
We show for $2\le p<\infty $ and subspaces $X$ of quotients of $L_{p}$ with a $1$-unconditional finite-dimensional Schauder decomposition that $K(X,\ell _{p})$ is an $M$-ideal in $L(X,\ell _{p})$.
We study the position of compact operators in the space of all continuous linear operators and its subspaces in terms of ideals. One of our main results states that for Banach spaces $X$ and $Y$ the subspace of all compact operators $\mathcal K(X,Y)$ is an $M(r_1 r_2, s_1 s_2)$-ideal in the space of all continuous linear operators $\mathcal L(X,Y)$ whenever $\mathcal K(X,X)$ and $\mathcal K(Y,Y)$ are $M(r_1,s_1)$- and $M(r_2,s_2)$-ideals in $\mathcal L(X,X)$ and $\mathcal L(Y,Y)$, respectively, with $r_1+s_1/2>1$ and $r_2+s_2/2>1$. We also prove that the $M(r,s)$-ideal $\mathcal K(X,Y)$ in $\mathcal L(X,Y)$ is separably determined. Among others, our results complete and improve some well-known results on $M$-ideals.
In analogy with effect algebras, we introduce the test spaces and $MV$-test spaces. A test corresponds to a hypothesis on the propositional system, or, equivalently, to a partition of unity. We show that there is a close correspondence between $MV$-algebras and $MV$-test spaces.
In this paper, we study the existence of the $n$-flat preenvelope and the $n$-FP-injective cover. We also characterize $n$-coherent rings in terms of the $n$-FP-injective and $n$-flat modules.
We introduce the notion of weak dually residuated lattice ordered semigroups (WDRL-semigroups) and investigate the relation between $R_0$-algebras and WDRL-semigroups. We prove that the category of $R_0$-algebras is equivalent to the category of some bounded WDRL-semigroups. Moreover, the connection between WDRL-semigroups and DRL-semigroups is studied.
We observe that a separable Banach space $X$ is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if $\mathcal L(X,Y)$ is not reflexive for reflexive $X$ and $Y$ then $\mathcal L(X_1, Y)$ is is not reflexive for some $X_1\subset X$, $X_1$ having a basis.
a1_Jednou z klíčových postav povídky Josefa Škvoreckého Malá pražská matahára (1955) je americký hudebník Robert Bulwer. Jeho statutu politického azylanta ,,vyhladovělí pražští fandové'' dovedně využijí k propašování jazzové revue na pražská pódia v době, kdy je tento žánr stále ještě považován za podezřelý. Fiktivní postava Bulwera má reálný předobraz v americkém jazzovém hráči na kontrabas Herbertu Wardovi (1921-1994), který spolu s manželkou, tanečnicí a choreografkou Jacqueline Wardovou (1919-2014) a dvěma syny požádal v roce 1954 o politický azyl v socialistickém Československu a poté do roku 1964 žil v Praze. Autor na základě odtajněných spisů amerického Federálního úřadu pro vyšetřování (FBI), ale i českých a jiných archivních pramenů a dobového tisku vykresluje životní příběh manželů Wardových, zejména jejich působení v Evropě, okolnosti získání azylu a život v Československu. Tento příběh zasazuje do kontextu pronásledování takzvané neamerické činnosti (mccarthismu) ve Spojených státech po vypuknutí studené války, kterým byla vedle jiných levicových umělců postižena také řada jazzových hudebníků a v němž shledává motivy k odchodu Wardových z Ameriky do Dánska v roce 1950. Značnou pozornost věnuje otázce členství Wardových v Komunistické straně USA a spřízněných levicových organizacích a důvodům zájmu FBI o jejich činnost., a2_V líčení jejich autora života v Praze poutá umělecké působení obou manželů, zejména Wardova revuální pásma přibližující pražskému publiku historii jazzu, a později v šedesátých letech jejich narůstající deziluze z pobytu v Československu, která je přivedla k návratu do USA. Stať je mimo jiné příspěvkem do nedávno započaté diskuse o anglicky mluvící levicové komunitě v Československu po začátku studené války a zároveň ilustruje práci FBI v době amerického mccarthismu., a1_One of the key characters of Josef Škvorecký´s short story Prague´s Little Mara Hara (1955) is an American musician named Robert Bulwer. ''Music-hungry fans of Prague'' skillfully use his political refugee´s status to smuggle a jazz revue onto stages of Prague at the time the music style is still viewed as something suspicious. The fictitious character of Bulwer was based on a realistic archetype, American double-bass jazz player Herbert Ward (1921-1994), who together with his wife, dancer and choreographer Jacqueline Ward (1919-2014) and two sons asked for political asylum in socialist Czechoslovakia in 1954 and then lived in Prague until 1964. Using declassified files of the US Federal Bureau of Investigation (FBI), but also information from Czech and other archival sources and period press, the author depicts the life story of the Wards, in particular their presence in Europe, circumstances under which the asylum was granted, and their life in Czechoslovakia. He sets the story into the context of persecution of so-called un-American activities (McCarthyism) in the United States after the outbreak of the Cold War; in addition to other left-wing artists, the campaign also affected many jazz musicians, and Petr Vidomus sees motives for the 1950 departure of the Wards from the USA to Denmark in it. He pays a lot of attention to the issue of the Wards´ membership in the Communist Party of the USA and related left-wing organizations and reasons of the FBI´s interest in their activities. Insofar as their life in Prague is concerned, the author is interested primarily in their artistic activities, in particular Herbert Ward´s revues describing the history of jazz to Prague´s audience, and later, in the 1960s, their disillusionment with the life in Czechoslovakia, which made them return to the United States., a2_The article is, inter alia, a contribution to a recently started discussion about the English-speaking left-wing community in Czechoslovakia after the beginning of the Cold War, and also illustrates the work of the FBI during the era of McCarthyism in the United States., Petr Vidomus., and Obsahuje bibliografii a bibliografické odkazy