Displaying similar documents to “Isomorphisms of Cartesian Products of ℓ-Power Series Spaces”

On the T -conditionality of T -power based implications

Zuming Peng (2022)

Kybernetika

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It is well known that, in forward inference in fuzzy logic, the generalized modus ponens is guaranteed by a functional inequality called the law of T -conditionality. In this paper, the T -conditionality for T -power based implications is deeply studied and the concise necessary and sufficient conditions for a power based implication I T being T -conditional are obtained. Moreover, the sufficient conditions under which a power based implication I T is T * -conditional are discussed, this discussions...

Bicrossed products of generalized Taft algebra and group algebras

Dingguo Wang, Xiangdong Cheng, Daowei Lu (2022)

Czechoslovak Mathematical Journal

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Let G be a group generated by a set of finite order elements. We prove that any bicrossed product H m , d ( q ) k [ G ] between the generalized Taft algebra H m , d ( q ) and group algebra k [ G ] is actually the smash product H m , d ( q ) k [ G ] . Then we show that the classification of these smash products could be reduced to the description of the group automorphisms of G . As an application, the classification of H m , d ( q ) k [ C n 1 × C n 2 ] is completely presented by generators and relations, where C n denotes the n -cyclic group.

On non-normality points, Tychonoff products and Suslin number

Sergei Logunov (2022)

Commentationes Mathematicae Universitatis Carolinae

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Let a space X be Tychonoff product α < τ X α of τ -many Tychonoff nonsingle point spaces X α . Let Suslin number of X be strictly less than the cofinality of τ . Then we show that every point of remainder is a non-normality point of its Čech–Stone compactification β X . In particular, this is true if X is either R τ or ω τ and a cardinal τ is infinite and not countably cofinal.

Σ s -products revisited

Reynaldo Rojas-Hernández (2015)

Commentationes Mathematicae Universitatis Carolinae

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We show that any Σ s -product of at most 𝔠 -many L Σ ( ω ) -spaces has the L Σ ( ω ) -property. This result generalizes some known results about L Σ ( ω ) -spaces. On the other hand, we prove that every Σ s -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every Σ s -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...

Unicellularity of the multiplication operator on Banach spaces of formal power series

B. Yousefi (2001)

Studia Mathematica

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Let β ( n ) n = 0 be a sequence of positive numbers and 1 ≤ p < ∞. We consider the space p ( β ) of all power series f ( z ) = n = 0 f ̂ ( n ) z such that n = 0 | f ̂ ( n ) | p | β ( n ) | p < . We give some sufficient conditions for the multiplication operator, M z , to be unicellular on the Banach space p ( β ) . This generalizes the main results obtained by Lu Fang [1].

On butterfly-points in β X , Tychonoff products and weak Lindelöf numbers

Sergei Logunov (2022)

Commentationes Mathematicae Universitatis Carolinae

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Let X be the Tychonoff product α < τ X α of τ -many Tychonoff non-single point spaces X α . Let p X * be a point in the closure of some G X whose weak Lindelöf number is strictly less than the cofinality of τ . Then we show that β X { p } is not normal. Under some additional assumptions, p is a butterfly-point in β X . In particular, this is true if either X = ω τ or X = R τ and τ is infinite and not countably cofinal.

On sums and products in a field

Guang-Liang Zhou, Zhi-Wei Sun (2022)

Czechoslovak Mathematical Journal

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We study sums and products in a field. Let F be a field with ch ( F ) 2 , where ch ( F ) is the characteristic of F . For any integer k 4 , we show that any x F can be written as a 1 + + a k with a 1 , , a k F and a 1 a k = 1 , and that for any α F { 0 } we can write every x F as a 1 a k with a 1 , , a k F and a 1 + + a k = α . We also prove that for any x F and k { 2 , 3 , } there are a 1 , , a 2 k F such that a 1 + + a 2 k = x = a 1 a 2 k .

The weak Gelfand-Phillips property in spaces of compact operators

Ioana Ghenciu (2017)

Commentationes Mathematicae Universitatis Carolinae

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For Banach spaces X and Y , let K w * ( X * , Y ) denote the space of all w * - w continuous compact operators from X * to Y endowed with the operator norm. A Banach space X has the w G P property if every Grothendieck subset of X is relatively weakly compact. In this paper we study Banach spaces with property w G P . We investigate whether the spaces K w * ( X * , Y ) and X ϵ Y have the w G P property, when X and Y have the w G P property.