Wyniki wyszukiwania

1

Rearrangement of series in nonnuclear spaces

100%

Banaszczyk W.

Studia Mathematica

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1993

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tom 107

|

nr 3

213-222

EN

It is proved that if a metrizable locally convex space is not nuclear, then it does not satisfy the Lévy-Steinitz theorem on rearrangement of series.

2

Balancing vectors and convex bodies

100%

Banaszczyk W.

Studia Mathematica

|

1993

|

tom 106

|

nr 1

93-100

EN

Let U, V be two symmetric convex bodies in $ℝ^n$ and |U|, |V| their n-dimensional volumes. It is proved that there exist vectors $u_1,...,u_n ∈ U$ such that, for each choice of signs $ε_1,...,ε_n = ± 1$, one has $ε_1 u_1 + ... + ε_n u_n ∉ rV$ where $r = (2πe^2)^{-1/2} n^{1/2}(|U|/|V|)^{1/n}$. Hence it is deduced that if a metrizable locally convex space is not nuclear, then it contains a null sequence $(u_n)$ such that the series $∑_{n = 1}^∞ ε_n u_{π(n)}$ is divergent for any choice of signs $ε_n = ± 1$ and any permutation π of indices.

3

Summable families in nuclear groups

100%

Banaszczyk W.

Studia Mathematica

|

1993

|

tom 105

|

nr 3

271-282

EN

Nuclear groups form a class of abelian topological groups which contains LCA groups and nuclear locally convex spaces, and is closed with respect to certain natural operations. In nuclear locally convex spaces, weakly summable families are strongly summable, and strongly summable are absolutely summable. It is shown that these theorems can be generalized in a natural way to nuclear groups.

4

On the lattice of polynomials with integer coefficients: the covering radius in $L_p(0,1)$

64%

Banaszczyk W., Lipnicki A.

Annales Polonici Mathematici

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2015

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tom 115

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nr 2

123-144

EN

The paper deals with the approximation by polynomials with integer coefficients in $L_p(0,1)$, 1 ≤ p ≤ ∞. Let $P_{n,r}$ be the space of polynomials of degree ≤ n which are divisible by the polynomial $x^r(1-x)^r$, r ≥ 0, and let $P_{n,r}^ℤ ⊂ P_{n,r}$ be the set of polynomials with integer coefficients. Let $μ(P_{n,r}^ℤ;L_p)$ be the maximal distance of elements of $P_{n,r}$ from $P_{n,r}^ℤ$ in $L_p(0,1)$. We give rather precise quantitative estimates of $μ(P_{n,r}^ℤ;L₂)$ for n ≳ 6r. Then we obtain similar, somewhat less precise, estimates of $μ(P_{n,r}^ℤ;L_p)$ for p ≠ 2. It follows that $μ(P_{n,r}^ℤ;L_p) ≍ n^{-2r-2/p}$ as n → ∞. The results partially improve those of Trigub [Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962)].

5

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On the existence of commutative Banach-Lie groups which do not admit continuous unitary representations

63%

Banaszczyk W.

Colloquium Mathematicum

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1987

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tom 52

|

nr 1

113-118

6

On the existence of unitary representations of commutative nuclear Lie groups

44%

Banaszczyk W.

Studia Mathematica

|

1983

|

tom 76

|

nr 2

175-181

7

Closed subgroups of nuclear spaces are weakly closed

38%

Banaszczyk W.

Studia Mathematica

|

1984

|

tom 80

|

nr 2

119-128

Ograniczanie wyników

5 Studia Mathematica

1 Annales Polonici Mathematici

1 Colloquium Mathematicum

7 Banaszczyk W.

1 Lipnicki A.

1 2015

3 1993

1 1987

1 1984

1 1983

Rearrangement of series in nonnuclear spaces

Balancing vectors and convex bodies

Summable families in nuclear groups

On the lattice of polynomials with integer coefficients: the covering radius in $L_p(0,1)$

On the existence of commutative Banach-Lie groups which do not admit continuous unitary representations

On the existence of unitary representations of commutative nuclear Lie groups

Closed subgroups of nuclear spaces are weakly closed