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Homotopy commutativity in symmetric spaces
We extend previous results of Ganea and the two of the authors with Takeda on the homotopy commutativity of the loop spaces of Hermitian symmetric...
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The Hardy-Littlewood Inequalities in Sequence Spaces
The investigation of the relation between the sums of coefficients of bilinear forms on c 0 × c 0 and their supremum norms was initiated in 1930 by...
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The Geometric Surgery Exact Sequence
In this chapter we introduce the surgery exact sequence, see Theorem 11.22 and Remark 11.23. It is the realisation of the Surgery Program, which we...
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Metric Spaces
Metric space is a set X together with a nonnegative real-valued function of X × X that defines the notion of “distance” between each pair of points...
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Models of Self-Adjoint and Unitary Operators in Pontryagin Spaces
This article is a revised version of the lectures given by the author at KROMSH-2019. These lectures are devoted to describing a few different ways...
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Real Structure in Operator Spaces, Injective Envelopes and G-spaces
We present some more foundations for a theory of real structure in operator spaces and algebras, in particular concerning the real case of the theory...
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Lorentz spaces depending on more than two parameters
For more than 50 years, the author has asked himself why Lorentz spaces are only defined for two parameters. Has this choice been made just for...
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Hadamard weighted geometric mean inequalities for the spectral and essential spectral radius of positive operators on Banach function and sequence spaces
We prove new inequalities for the spectral radius, essential spectral radius, operator norm, measure of noncompactness and numerical radius of...
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Variable Besov-type Spaces
In this paper we introduce Besov-type spaces with variable smoothness and integrability. We show that these spaces are characterized by the...
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Lipschitz geometry of operator spaces and Lipschitz-free operator spaces
We show that there is an operator space notion of Lipschitz embeddability between operator spaces which is strictly weaker than its linear...
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On paranormed Ideal convergent sequence spaces defined by Jordan totient function
The study of sequence spaces and summability theory has been an important aspect in defining new notions of convergence for the sequences that do not...
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Product type operators acting between weighted Bergman spaces and Bloch type spaces
For analytic functions u , ψ in the unit disk ⅅ in the complex plane and an analytic self-map φ of ⅅ, we describe in this paper the boundedness and...
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Applications of ball spaces theory: fixed point theorems in semimetric spaces and ball convergence
In the paper, we apply some of the results from the theory of ball spaces in semimetric setting. This allows us to obtain fixed point theorems which...
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Approximation in modified Zorko spaces
The set of smooth functions is not dense in Morrey spaces. To address the density issue in Morrey spaces, Zorko spaces are defined by utilizing the...
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Existence of coincidence and common fixed points for a sequence of map**s in quasi partial metric spaces
Till now, there exists enormous literature showing existence of fixed points using expansive map**s. But the existence of common and coincidence...
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Nonlinear expansions in Banach spaces
We introduce an expansion scheme in Banach spaces, which is a generalization of the known expansion method for Reproducing Kernel Hilbert Spaces...