## Textbook covering superoperators and tensor products

I am looking for a textbook to cover the following areas:

• Tensor products of Hilbert spaces
• Tensor products of operators on Hilbert spaces (i.e., something like $$A\otimes B$$ is the operator with $$(A\otimes B)(\psi\otimes\phi)=A\psi\otimes B\phi$$).
• Tensor products of superoperators (i.e., linear functions from operators to operators, e.g., $$\mathcal E\otimes\mathcal F$$ defined by $$(\mathcal E\otimes\mathcal F)(\rho\otimes\sigma)=\mathcal E(\rho)\otimes\mathcal F(\sigma)$$ for trace-class operators $$\rho,\sigma$$).

Background: tensor products of (completely positive trace-preserving) superoperators would correspond to composing quantum channels.

The text should be a mathematically rigorous textbook, and not limited only to finite or separable Hilbert spaces. I have found textbooks covering the first two points to varying degrees, but nothing for the third one.

I need it as a reference for citing in a research paper.

## How to Increase file size of Importing Products to Magento 2

I’m looking to import product into M2 but the allowed size is 2MB and my file has 2.33 MB how can I increase the size?

## SEO and number of products per page

I’m curious if the numbers of products displayed on a page would effect seo. It would seems like a page with more products might have an advantage as it has more keywords and images displayed. But then how many would be too many? I’ve visited some sites where you scroll down and more and more products load and it just slows down. I have a page that currently only displays 12 products per page getting beat in rankings by a page that has like 21 products. Looking for any thoughts on if more products might be an advantage and how many might be too many.

## How to set a color swatches for Simple Products in Magento2?

Is there any way to set a color swatches in Simple Product Types. Please suggest me a way.

Any help would be appreciated.

## Magento 2.3 – Products URL key regenerate on import functionality

I update the products with no url_key header present (only sku,description) using the import functionality

The import should only update the fields which are mentioned in the CSV file.

The import removes the URL keys from admin against every sku mentioned in the CSV and URL keys regenerate from the name against each product sku.

I have got collection in $collecction from Magento\Catalog\Model\ResourceModel\Product\CollectionFactory with some certain conditions I am updating a custom attribute viewed_count in foreach loop like this: foreach($  collection as $k=>$  _product){     echo $_product->getSku()." ";$  viewCount = $this->getViewedCount($  _product->getId());     $_product->getResource()->saveAttribute($  _product, "viewed_count");     $_product->setViewedCount($  viewCount);     $_product->save(); }  After this it is successfully updating product viewed count in viewed_count attribute. But the issue is: After this code is executed, all other attributes got updated and set to some default values. Can anyone tell me what am I doing wrong? ## Is it even possible to prototype chrome extension products in Invision? Without giving away too much IP I am starting work on prototyping a product that augments google chrome with notifications and menus through an extension. From what I can tell, there seems to be no possible way for me to construct a prototype with any current prototyping tool due to a core issue. I cannot use GIFs/Videos of a person using chrome as a background in Invision and overlay my product over it. Because of this problem, I have to take videos of Invision animations and components and overlay them on a video on me using chrome. This is not a dynamic system that can evolve over time, and is not interactive at all. What tools can I use to actually create a demo of this product? I am a first time PM intern so sorry if this seems dumb but my company is at a standstill in product development due to this problem. ## magento 2 add associate Simple Products with custom options to Configurable Product not working I want to add the simple products with custom options to configurable product.When I am trying to add the simple product to configurable product, it’s not showing after product save.Need suggestion to achieve this . I am created ## Import Orders to magento no stock products Trying to import orders to magento from other platform. I have almost done except import products with attribute stock_data is_in_stock set to 0. If I set manually the value to 1 imports correctly. I’ve tried it setting the value temporally to 1 and once is imported set it to 0 when needed, but i think is not the best way. Is there any other way to do it? any help will be appreciated. function _order_create($  data){         if(is_array($data) and !empty($  data['product'])){             $quote = Mage::getModel('sales/quote') ->setStoreId(Mage::app()->getStore('default')->getId());$  customer = Mage::getModel('customer/customer')                             ->setWebsiteId(1)                             ->loadByEmail($data['customer_email']);$  quote->assignCustomer($customer); // add product(s) foreach ($  data['product'] as $id =>$  pdata) {                  $product = Mage::getModel('catalog/product')->load($  pdata['id']);                 $buyInfo = array('qty' =>$  pdata['qty']); //****************** here set is_in_stock to 1                 $quote->addProduct($  product, new Varien_Object($buyInfo));$  quote->save(); // without saving the quote here I get error                  $quoteItem =$  quote->getItemByProduct($product);$  quoteItem->setOriginalCustomPrice($pdata['price']);$  quoteItem->setCustomPrice($pdata['price']);$  quoteItem->setIsSuperMode(true);                 $quoteItem->save(); // ****************** here set is_in_stock to 0 } foreach ($  data['address']['shipping'] as $key =>$  value) {                 $addressDataShipping[$  key] = $value; } foreach ($  data['address']['billing'] as $key =>$  value) {                 $addressDataBilling[$  key] = $value; }$  billingAddress = $quote->getBillingAddress()->addData($  addressDataBilling);             $shippingAddress =$  quote->getShippingAddress()->addData($addressDataShipping);$  shippingAddress->setCollectShippingRates(true)->collectShippingRates()                             ->setShippingMethod($data['methods']['shipping']) ->setPaymentMethod($  data['methods']['payment']);              $quote->getPayment()->importData(array('method' =>$  data['methods']['payment']));             $quote->setTotalsCollectedFlag(false)->collectTotals()->save();$  service = Mage::getModel('sales/service_quote', $quote);$  service->submitAll();              $order =$  service->getOrder();             $order->setCreatedAt($  data['order']['createdat']);             $order->setData('state',$  data['order']['status']);             $order->setStatus($  data['order']['status']);                     $order->save(); //printf("Created order %s\n",$  order->getIncrementId());         }     } 

This is the method im using

Let $$\sigma$$ $$\in$$ $$Aut(M)$$, Does $$\sigma$$ extend to automorphism to $$M\rtimes_{\alpha} G$$? If it is, what is the extension map?