For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and‎ ‎a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$‎, ‎it is shown that the strong Banach-Saks-ness of all evaluation‎ ‎operators on ${mathcal M}$ is a sufficient condition for the weak‎ ‎Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in‎ ‎Y^*$‎, ‎the evaluation op...

It is well known that subspace identification methods that assume open loop data without correlations between the input and noise, may give biased estimates when applied to closed loop data. The effect of the controller gain parameters on the quality of the identified model is studied when closed loop data are used. Several subspace identification methods (both open loop and closed loop methods...

We study relations between certain totally geodesic foliations of a closed flat manifold and its collapsed Gromov-Hausdorff limits. Our main results explicitly identify such limits as orbifolds, provide algebraic geometric criteria to determine whether they are singular.

It is known that many subspace algorithms give biased estimates for closed-loop data due to the existence of feedback. In this paper we present a new subspace identification method using the parity space employed in fault detection in the past. The basic algorithm, known as subspace identification method via principal component analysis (SIMPCA), gives consistent estimation of the deterministic...

2 Description of the topic Closed loop identification has always been recognized to be of primary importance and has been object of intense research since the late sixties. It is recognized that most of the times feedback cannot be removed for various reasons among which: (i) it may be intrinsic in the physical mechanism generating the data or (ii) data may come from an industrial plant where f...

in proposition 2.6 in (g‎. ‎gruenhage‎, ‎a‎. ‎lutzer‎, ‎baire and volterra spaces‎, ‎textit{proc‎. ‎amer‎. ‎math‎. ‎soc.} {128} (2000)‎, ‎no‎. ‎10‎, ‎3115--3124) a condition that‎ ‎every point of $d$ is $g_delta$ in $x$ was overlooked‎. ‎so we‎ ‎proved some conditions by which a baire space is equivalent to a‎ ‎volterra space‎. ‎in this note we show that if $x$ is a‎ ‎monotonically normal $t_1$...

In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed Gδ subspace.

for suitable banach spaces $x$ and $y$ with schauder decompositions and‎ ‎a suitable closed subspace $mathcal{m}$ of some compact operator space from $x$ to $y$‎, ‎it is shown that the strong banach-saks-ness of all evaluation‎ ‎operators on ${mathcal m}$ is a sufficient condition for the weak‎ ‎banach-saks property of ${mathcal m}$, where for each $xin x$ and $y^*in‎ ‎y^*$‎, ‎the evaluation op...