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Bibliographic Details
Main Authors:	Abrahamsen, Trond A., Aliaga, Ramón J., Lima, Vegard, Martiny, André, Perreau, Yoël, Prochazka, Antonín, Veeorg, Triinu
Format:	Preprint
Published:	2023
Subjects:	Functional Analysis
Online Access:	https://arxiv.org/abs/2303.00511
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On Weak Compactness and Uniform Regularity in Lipschitz free Spaces
by: Aliaga, Ramón J., et al.
Published: (2025)

Duality of Lipschitz-free spaces over ultrametric spaces
by: Abrahamsen, Trond A., et al.
Published: (2025)

A Banach space with an unconditional basis which is not slicely countably determined
by: Lõo, Marcus, et al.
Published: (2026)

A note on nonseparable Lipschitz-free spaces
by: Aliaga, Ramón J., et al.
Published: (2023)

Strictly convex norms and the local diameter two property
by: Abrahamsen, Trond A., et al.
Published: (2024)

Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and $Δ$-points
by: Cobollo, Christian, et al.
Published: (2023)

The Daugavet property is equivalent to the polynomial Daugavet property
by: Dantas, Sheldon, et al.
Published: (2025)

The super Alternative Daugavet property for Banach spaces
by: Langemets, Johann, et al.
Published: (2025)

The Daugavet and Delta-constants of points in Banach spaces
by: Choi, Geunsu, et al.
Published: (2023)

On metric characterizations of tree and fragmentability indices of Banach spaces
by: Basset, Estelle, et al.
Published: (2026)

The metric geometry of subspaces and convex cones of the Banach space revisited
by: Németh, A. B.
Published: (2025)

Lipschitz spaces over non-porous sets
by: Aliaga, Ramón J.
Published: (2025)

Slicely countably determined points in Banach spaces
by: Langemets, Johann, et al.
Published: (2023)

Diversity of Lipschitz-free spaces over countable complete discrete metric spaces
by: Basset, Estelle, et al.
Published: (2025)

A solution to the extreme point problem and other applications of Choquet theory to Lipschitz-free spaces
by: Aliaga, Ramón J., et al.
Published: (2024)

Uniformly nonsquare Banach spaces have the fixed point property 1
by: Dalby, Tim
Published: (2024)

Lipschitz extension and Lipschitz-free spaces over nets in normed spaces
by: Aliaga, Ramón J., et al.
Published: (2026)

Fixed point results for multivalued mapping with closed graphs in generalized Banach spaces
by: Amara, Khaled Ben, et al.
Published: (2022)

On greedy approximation in complex Banach spaces
by: Gasnikov, A., et al.
Published: (2024)

On coarse geometry of separable dual Banach spaces
by: Jackson, Stephen, et al.
Published: (2025)

On Chebyshev centers in Banach spaces
by: Das, Syamantak, et al.
Published: (2025)

Characterizations of reflexive Banach spaces
by: Zhou, Tianyi
Published: (2025)

Summability Methods for the Greedy Algorithm in Banach spaces
by: Berasategui, Miguel, et al.
Published: (2025)

Pełczyński's property (V$^*$) in Lipschitz-free spaces
by: Aliaga, Ramón J., et al.
Published: (2024)

A note on summability in Banach spaces
by: Rodríguez, José
Published: (2024)

Operators with the Kato property on Banach spaces
by: Sevilla, Mar Jiménez, et al.
Published: (2025)

Isometries of Lipschitz-free Banach spaces
by: Cúth, Marek, et al.
Published: (2024)

The ZOO of combinatorial Banach spaces
by: Borodulin-Nadzieja, Piotr, et al.
Published: (2024)

In which Banach spaces is the polar of every convex cone convex
by: Németh, A. B.
Published: (2025)

On some properties of modulation spaces as Banach algebras
by: Feichtinger, Hans G., et al.
Published: (2024)

A generalised mid summability in Banach spaces
by: Philip, Aleena, et al.
Published: (2024)

Dynamics on weighted solid Banach function spaces
by: Ivkovic, Stefan
Published: (2025)

Equivalence of D and D' properties in Banach spaces
by: Enabe, Paulo Akira F.
Published: (2024)

Transfinite (almost isometric) ideals in Banach spaces
by: Vañó, Esteban Martínez, et al.
Published: (2025)

Further study of modulation spaces as Banach algebras
by: Feichtinger, Hans G., et al.
Published: (2024)

Semi denting points and related notions in Banach spaces
by: Basu, Sudeshna, et al.
Published: (2026)

Construction of generalized samplets in Banach spaces
by: Balazs, Peter, et al.
Published: (2024)

Fekete's lemma in Banach spaces
by: Kulikov, Aleksei, et al.
Published: (2024)

Packings in classical Banach spaces
by: De Bernardi, Carlo Alberto, et al.
Published: (2026)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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