Classification of General Sequences by Frame-Related Operators

This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We investigate these operators for arbitrary sequences, which in general lead to possibly unbounded operators. We characterize various classes of sequences in terms of these operators and vice-versa. Finally, we classify these sequences by operators applied on orthonormal bases

On Various R-duals and the Duality Principle

The duality principle states that a Gabor system is a frame if and only if the corresponding adjoint Gabor system is a Riesz sequence. In general Hilbert spaces and without the assumption of any particular structure, Casazza, Kutyniok and Lammers have introduced the so-called R-duals that also lead to a characterization of frames in terms of associated Riesz sequences; however, it is still an open question whether this abstract theory is a generalization of the duality principle. In this paper we prove that a modified version of the R-duals leads to a generalization of the duality principle that keeps all the attractive properties of the R-duals. In order to provide extra insight into the relations between a given sequence and its R-duals, we characterize all the types of R-duals that are available in the literature for the special case where the underlying sequence is a Riesz basis

Listeriosis in Neonates - A Microbiological Study

About the important lore of Listeria monocytogenes as an etiological agent of 3 cases of neonatal infection in Varna City during the period 2002-2003. The etiological diagnosis is based on detection the microorganism in blood cultures, nasopharyngeal and other secretions, obtained from newborns. L. monocytogenes is isolated and identified by the conventional methods. Some microbiological laboratorial aspects are reported. Listeria monocytogenes is one of the six species of genus Listeria. It is a human pathogen of high public health concern. Diseases, caused by this microorganism affect some groups of patients, who are especially ssusceptible - elderly patients, immunocompromised patients, pregnant women and neonates. L. monocytogenes often causes an influenza - like illnes that, if untreatened may lead to infection of the fetus, resulting in abortion, stillbirth or premature birth, because it is able to cross the placenta. Neonatal infection is divided into early (less than 2 days old), intermediate (305 days old) and late (more than 5 days old) onset disease. Early neonatal listeriosis is predominantly a septicaemic illnes, contracted in utero. In contrast, late onset disease represents a spectrum of mild to severe infection, which can be correlated with the microbiological findings. The main sites of isolation are blood, superficial sites and amniotic fluid, less commonly gastric aspirate, cerebrospinal fluid (CSF) and high vaginal swabs. The main site of isolation of L. monocytogenes for the late onset disease os CSF commonly and rarely blood

Fr\'echet frames, general definition and expansions

We define an {\it $(X_1,\Theta, X_2)$-frame} with Banach spaces $X_2\subseteq X_1$, $|\cdot|_1 \leq |\cdot|_2$, and a $BK$-space (\Theta, \snorm[\cdot]). Then by the use of decreasing sequences of Banach spaces ${X_s}_{s=0}^\infty$ and of sequence spaces ${\Theta_s}_{s=0}^\infty$, we define a general Fr\' echet frame on the Fr\' echet space $X_F=\bigcap_{s=0}^\infty X_s$. We give frame expansions of elements of $X_F$ and its dual $X_F^*$, as well of some of the generating spaces of $X_F$ with convergence in appropriate norms. Moreover, we give necessary and sufficient conditions for a general pre-Fr\' echet frame to be a general Fr\' echet frame, as well as for the complementedness of the range of the analysis operator $U:X_F\to\Theta_F$.Comment: A new section is added and a minor revision is don