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.
The authors consider the changes in the conception, organization, ways of spending, and forms of leisure in the Czech Lands from the establishment of the Communist monopoly on power in early 1948 to the second half of the 1950s. (After this point leisure time here began strikingly to change under the infl uence of consumerist trends.) They consider the topic in the context of the dominant ideology and changes in economic, social, and arts policies. The authors take into account gender differences, contrasts between town and country, and special features of social groups. They pay particular attention to leisure amongst young people and children. The authors do not, however, see the Communist takeover of February 1948 as a watershed in the sphere of leisure. Instead, they demonstrate both the continuity and differences between the period of limited democracy, from May 1945 to February 1948, and the years that followed. In some cases, they highlight features that were identical in Nazi German and Communist approaches to leisure activities (the rejection of jazz, ''trash'' (brak) in the arts, and Western infl uences in general). The authors discuss how the Communist regime intervened intensively in the way people chose to spend their free time, in its endeavour to shape a new type of man and woman in the new social conditions. At the same time, particularly in the late 1940s and early 1950s, the State so emphasized the importance of the work of building socialism, that leisure was seen as a ''necessary evil'', since it used up valuable physical and mental energy that would have been better spent on increasing productivity. For the same aims, but also with regard to the idea of somewhatdemocratising the arts, the regime gave preference to activities such as political and vocational self-education as well as the study of selected arts and cultural values. In keeping with the subordination of the individual to the interests of society, collective forms of recreation and the leisure (holidays spent with groups of co-workers, mass group visits to plays, fi lms, concerts, museums, galleries, and, later, Pioneer camps) were given priority. Traditional club activity and individual leisure were seen as ''bourgeois survivals''. Some young people’s non-conformist leisure activities met with suspicion from the authorities or with outright repression. Amongst the models of leisure that the regime held worthy of emulation were the Socialist youth construction projects (stavby mládeže), ''volunteer'' work, and additional instruction or training. The new organizations, such as the Revolutionary Trades Union Movement (Revoluční odborové hnutí - ROH), the Czechoslovak Union of Youth (Československý svaz mládeže - ČSM), and the Union for Co-operation with the Army (Svaz pro spolupráci s armádou - Svazarm), which took the place of the earlier clubs and associations, comported with the new ideology and provided the required forms of leisure. The authorities endeavoured also to support considerably developed and differentiated hobbies, such as making art, playing board games, and collecting. Special facilities were established to run these activities, including the enterprise-based clubs of the ROH, houses of culture (kulturní domy), and people’s educational societies (osvětové besedy). Forms of universally accessible activity, like chess and phillumeny (collecting matchbox labels), were supported, whereas fi nancially more demanding hobbies or those linked to private gain, such as philately or numismatics, were marginalized. A slight retreat from the ideologised conception of leisure came with the so-called ''new course'' of 1953. But more striking changes were made in the second half of the 1950s. These years, which saw shorter working weeks, a higher standard of living than before, and the emergence of consumerist trends, are described by the authors as a period of the planned expansion of leisure and its gradual individualisation.
The study deals with issues of corporate management and pitfalls of the ''socialist supervision'' in Czechoslovak enterprises in the period of late socialism. Using documents of the Communist Party of Czechoslovakia and the State Security, period texts and specialized publications, it shows how party organs and state authorities were unsuccessfully trying to make supervisory mechanisms and audits a functional tool of the implementation of the ruling party´s economic policy. The author analyzes the supervisory and audit mechanisms that were used, and outlines basic reasons of the almost fatal failure of supervisory activities of the system which was, in a way, obsessed with supervision and control. He explains the systemic conditionality of the supervisory system which socialist managers often and in many respects bent to suit the needs of the enterprises they were in charge of; such situation naturally did not match the needs of the society as a whole. Using many specifi c cases as an example, the study graphically shows that members of the Czechoslovak corporate management community in the 1980s were fully aware of systemic, political and social limitations of the supervisory system which they managed to modify, fairly successfully, to suit intra-corporate conditions. The result was a situation in which the party leadership was reacting to increasingly obvious symptoms of the “agony of the centrally planned economy” by adopting various directives and guidelines to make the supervisory process more effective and to consistently promote the ''whoever manages - supervises'' principle. However, the anticipated effect did not materialize and, at the end of the day, the non-functional supervisory mechanisms made a substantial contribution to the collapse of the Communist regime in Czechoslovakia. and Překlad: Jiří Mareš